LMFDB - Embedded newform 162.2.g.a.7.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,2,Mod(7,162)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([16]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("162.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	162.g (of order $27$, degree $18$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.29357651274$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$4$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			7.2
Character	$\chi$	$=$	162.7
Dual form			162.2.g.a.139.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.597159 - 0.802123i) q^{2} +(-1.45578 - 0.938458i) q^{3} +(-0.286803 + 0.957990i) q^{4} +(-1.84048 + 1.21050i) q^{5} +(0.116573 + 1.72812i) q^{6} +(-0.500394 + 0.530386i) q^{7} +(0.939693 - 0.342020i) q^{8} +(1.23859 + 2.73238i) q^{9} +O(q^{10})$	\(q+(-0.597159 - 0.802123i) q^{2} +(-1.45578 - 0.938458i) q^{3} +(-0.286803 + 0.957990i) q^{4} +(-1.84048 + 1.21050i) q^{5} +(0.116573 + 1.72812i) q^{6} +(-0.500394 + 0.530386i) q^{7} +(0.939693 - 0.342020i) q^{8} +(1.23859 + 2.73238i) q^{9} +(2.07003 + 0.753431i) q^{10} +(-4.52549 + 2.27279i) q^{11} +(1.31656 - 1.12547i) q^{12} +(1.20347 + 2.78995i) q^{13} +(0.724249 + 0.0846526i) q^{14} +(3.81535 - 0.0350123i) q^{15} +(-0.835488 - 0.549509i) q^{16} +(-0.217267 + 0.182309i) q^{17} +(1.45207 - 2.62517i) q^{18} +(-0.414317 - 0.347653i) q^{19} +(-0.631794 - 2.11034i) q^{20} +(1.22621 - 0.302527i) q^{21} +(4.52549 + 2.27279i) q^{22} +(-2.07953 - 2.20417i) q^{23} +(-1.68896 - 0.383956i) q^{24} +(-0.0583439 + 0.135256i) q^{25} +(1.51922 - 2.63137i) q^{26} +(0.761105 - 5.14011i) q^{27} +(-0.364590 - 0.631488i) q^{28} +(-7.83856 + 0.916196i) q^{29} +(-2.30645 - 3.03947i) q^{30} +(-6.13355 + 1.45368i) q^{31} +(0.0581448 + 0.998308i) q^{32} +(8.72104 + 0.938307i) q^{33} +(0.275977 + 0.0654077i) q^{34} +(0.278931 - 1.58190i) q^{35} +(-2.97282 + 0.402903i) q^{36} +(-0.756289 - 4.28913i) q^{37} +(-0.0314478 + 0.539938i) q^{38} +(0.866269 - 5.19096i) q^{39} +(-1.31547 + 1.76698i) q^{40} +(2.85024 - 3.82854i) q^{41} +(-0.974905 - 0.802913i) q^{42} +(0.374544 - 6.43067i) q^{43} +(-0.879381 - 4.98722i) q^{44} +(-5.58716 - 3.52957i) q^{45} +(-0.526208 + 2.98428i) q^{46} +(11.1130 + 2.63384i) q^{47} +(0.700595 + 1.58403i) q^{48} +(0.376098 + 6.45735i) q^{49} +(0.143333 - 0.0339705i) q^{50} +(0.487382 - 0.0615053i) q^{51} +(-3.01790 + 0.352742i) q^{52} +(4.27064 + 7.39697i) q^{53} +(-4.57750 + 2.45896i) q^{54} +(5.57787 - 9.66116i) q^{55} +(-0.288813 + 0.669545i) q^{56} +(0.276897 + 0.894926i) q^{57} +(5.41577 + 5.74038i) q^{58} +(-9.12046 - 4.58047i) q^{59} +(-1.06071 + 3.66510i) q^{60} +(3.98650 + 13.3158i) q^{61} +(4.82873 + 4.05179i) q^{62} +(-2.06900 - 0.710332i) q^{63} +(0.766044 - 0.642788i) q^{64} +(-5.59221 - 3.67806i) q^{65} +(-4.45521 - 7.55567i) q^{66} +(-11.1908 - 1.30802i) q^{67} +(-0.112337 - 0.260426i) q^{68} +(0.958813 + 5.16034i) q^{69} +(-1.43544 + 0.720905i) q^{70} +(12.5701 + 4.57514i) q^{71} +(2.09842 + 2.14397i) q^{72} +(9.45983 - 3.44310i) q^{73} +(-2.98879 + 3.16793i) q^{74} +(0.211868 - 0.142150i) q^{75} +(0.451876 - 0.297203i) q^{76} +(1.05907 - 3.53755i) q^{77} +(-4.68109 + 2.40497i) q^{78} +(-4.78134 - 6.42245i) q^{79} +2.20288 q^{80} +(-5.93178 + 6.76860i) q^{81} -4.77300 q^{82} +(8.80861 + 11.8320i) q^{83} +(-0.0618626 + 1.26146i) q^{84} +(0.179191 - 0.598538i) q^{85} +(-5.38186 + 3.53970i) q^{86} +(12.2710 + 6.02238i) q^{87} +(-3.47523 + 3.68353i) q^{88} +(-3.62265 + 1.31854i) q^{89} +(0.505270 + 6.58931i) q^{90} +(-2.08196 - 0.757772i) q^{91} +(2.70799 - 1.36000i) q^{92} +(10.2933 + 3.63985i) q^{93} +(-4.52358 - 10.4868i) q^{94} +(1.18338 + 0.138317i) q^{95} +(0.852224 - 1.50788i) q^{96} +(-12.3125 - 8.09807i) q^{97} +(4.95500 - 4.15774i) q^{98} +(-11.8154 - 9.55030i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 9 q^{6}+O(q^{10}) $ 72 * q + 9 * q^6	$ 72 q + 9 q^{6} + 18 q^{13} - 9 q^{20} - 81 q^{23} + 18 q^{25} - 27 q^{26} - 27 q^{27} + 18 q^{28} - 27 q^{29} - 63 q^{30} - 54 q^{31} + 9 q^{33} - 27 q^{35} - 9 q^{36} + 9 q^{38} - 9 q^{41} + 9 q^{42} + 36 q^{43} - 117 q^{45} - 18 q^{46} - 27 q^{47} + 9 q^{48} - 27 q^{51} - 36 q^{52} - 27 q^{53} + 54 q^{55} + 27 q^{57} + 9 q^{58} - 18 q^{59} + 9 q^{63} + 9 q^{65} + 36 q^{66} - 135 q^{67} - 18 q^{68} + 108 q^{69} + 18 q^{70} + 72 q^{71} + 54 q^{72} + 36 q^{73} + 99 q^{74} - 36 q^{75} - 9 q^{76} + 144 q^{77} + 90 q^{78} - 9 q^{79} + 18 q^{80} - 72 q^{82} + 99 q^{83} + 18 q^{84} + 9 q^{85} + 72 q^{86} + 207 q^{87} - 9 q^{88} + 126 q^{89} - 18 q^{90} + 63 q^{91} + 36 q^{92} + 81 q^{93} + 18 q^{94} + 45 q^{95} - 171 q^{97} + 36 q^{98} + 99 q^{99}+O(q^{100}) $ 72 * q + 9 * q^6 + 18 * q^13 - 9 * q^20 - 81 * q^23 + 18 * q^25 - 27 * q^26 - 27 * q^27 + 18 * q^28 - 27 * q^29 - 63 * q^30 - 54 * q^31 + 9 * q^33 - 27 * q^35 - 9 * q^36 + 9 * q^38 - 9 * q^41 + 9 * q^42 + 36 * q^43 - 117 * q^45 - 18 * q^46 - 27 * q^47 + 9 * q^48 - 27 * q^51 - 36 * q^52 - 27 * q^53 + 54 * q^55 + 27 * q^57 + 9 * q^58 - 18 * q^59 + 9 * q^63 + 9 * q^65 + 36 * q^66 - 135 * q^67 - 18 * q^68 + 108 * q^69 + 18 * q^70 + 72 * q^71 + 54 * q^72 + 36 * q^73 + 99 * q^74 - 36 * q^75 - 9 * q^76 + 144 * q^77 + 90 * q^78 - 9 * q^79 + 18 * q^80 - 72 * q^82 + 99 * q^83 + 18 * q^84 + 9 * q^85 + 72 * q^86 + 207 * q^87 - 9 * q^88 + 126 * q^89 - 18 * q^90 + 63 * q^91 + 36 * q^92 + 81 * q^93 + 18 * q^94 + 45 * q^95 - 171 * q^97 + 36 * q^98 + 99 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{8}{27}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.597159	−	0.802123i	−0.422255	−	0.567187i
$2$	−0.597159	−	0.802123i	−0.422255	−	0.567187i
$3$	−1.45578	−	0.938458i	−0.840495	−	0.541819i
$3$	−1.45578	−	0.938458i	−0.840495	−	0.541819i
$4$	−0.286803	+	0.957990i	−0.143402	+	0.478995i
$5$	−1.84048	+	1.21050i	−0.823089	+	0.541354i	−0.889764	−	0.456421i	$-0.849131\pi$
$5$	−1.84048	+	1.21050i	−0.823089	+	0.541354i	0.0666753	+	0.997775i	$0.478761\pi$
$6$	0.116573	+	1.72812i	0.0475905	+	0.705503i
$7$	−0.500394	+	0.530386i	−0.189131	+	0.200467i	−0.815000	−	0.579461i	$-0.803263\pi$
$7$	−0.500394	+	0.530386i	−0.189131	+	0.200467i	0.625869	+	0.779928i	$0.284745\pi$
$8$	0.939693	−	0.342020i	0.332232	−	0.120922i
$9$	1.23859	+	2.73238i	0.412864	+	0.910793i
$10$	2.07003	+	0.753431i	0.654602	+	0.238256i
$11$	−4.52549	+	2.27279i	−1.36449	+	0.685272i	−0.972108	−	0.234532i	$-0.924644\pi$
$11$	−4.52549	+	2.27279i	−1.36449	+	0.685272i	−0.392379	+	0.919803i	$0.628348\pi$
$12$	1.31656	−	1.12547i	0.380057	−	0.324895i
$13$	1.20347	+	2.78995i	0.333782	+	0.773794i	0.999616	+	0.0276943i	$0.00881649\pi$
$13$	1.20347	+	2.78995i	0.333782	+	0.773794i	−0.665834	+	0.746100i	$0.731924\pi$
$14$	0.724249	+	0.0846526i	0.193564	+	0.0226244i
$15$	3.81535	−	0.0350123i	0.985118	−	0.00904014i
$16$	−0.835488	−	0.549509i	−0.208872	−	0.137377i
$17$	−0.217267	+	0.182309i	−0.0526950	+	0.0442163i	−0.668755	−	0.743483i	$-0.733172\pi$
$17$	−0.217267	+	0.182309i	−0.0526950	+	0.0442163i	0.616060	+	0.787699i	$0.288728\pi$
$18$	1.45207	−	2.62517i	0.342256	−	0.618758i
$19$	−0.414317	−	0.347653i	−0.0950509	−	0.0797572i	0.594024	−	0.804447i	$-0.297538\pi$
$19$	−0.414317	−	0.347653i	−0.0950509	−	0.0797572i	−0.689075	+	0.724690i	$0.741983\pi$
$20$	−0.631794	−	2.11034i	−0.141273	−	0.471886i
$21$	1.22621	−	0.302527i	0.267581	−	0.0660169i
$22$	4.52549	+	2.27279i	0.964839	+	0.484560i
$23$	−2.07953	−	2.20417i	−0.433611	−	0.459601i	0.473313	−	0.880894i	$-0.343058\pi$
$23$	−2.07953	−	2.20417i	−0.433611	−	0.459601i	−0.906925	+	0.421293i	$0.861576\pi$
$24$	−1.68896	−	0.383956i	−0.344757	−	0.0783747i
$25$	−0.0583439	+	0.135256i	−0.0116688	+	0.0270513i
$26$	1.51922	−	2.63137i	0.297945	−	0.516055i
$27$	0.761105	−	5.14011i	0.146475	−	0.989214i
$28$	−0.364590	−	0.631488i	−0.0689010	−	0.119340i
$29$	−7.83856	+	0.916196i	−1.45558	+	0.170133i	−0.806794	−	0.590833i	$-0.798799\pi$
$29$	−7.83856	+	0.916196i	−1.45558	+	0.170133i	−0.648791	+	0.760967i	$0.724725\pi$
$30$	−2.30645	−	3.03947i	−0.421098	−	0.554929i
$31$	−6.13355	+	1.45368i	−1.10162	+	0.261088i	−0.740919	−	0.671594i	$-0.765610\pi$
$31$	−6.13355	+	1.45368i	−1.10162	+	0.261088i	−0.360699	+	0.932682i	$0.617462\pi$
$32$	0.0581448	+	0.998308i	0.0102787	+	0.176478i
$33$	8.72104	+	0.938307i	1.51814	+	0.163338i
$34$	0.275977	+	0.0654077i	0.0473296	+	0.0112173i
$35$	0.278931	−	1.58190i	0.0471479	−	0.267389i
$36$	−2.97282	+	0.402903i	−0.495470	+	0.0671506i
$37$	−0.756289	−	4.28913i	−0.124333	−	0.705128i	−0.981702	−	0.190425i	$-0.939013\pi$
$37$	−0.756289	−	4.28913i	−0.124333	−	0.705128i	0.857369	−	0.514703i	$-0.172098\pi$
$38$	−0.0314478	+	0.539938i	−0.00510150	+	0.0875895i
$39$	0.866269	−	5.19096i	0.138714	−	0.831220i
$40$	−1.31547	+	1.76698i	−0.207994	+	0.279385i
$41$	2.85024	−	3.82854i	0.445133	−	0.597917i	−0.521763	−	0.853091i	$-0.674725\pi$
$41$	2.85024	−	3.82854i	0.445133	−	0.597917i	0.966895	+	0.255174i	$0.0821327\pi$
$42$	−0.974905	−	0.802913i	−0.150431	−	0.123892i
$43$	0.374544	−	6.43067i	0.0571174	−	0.980669i	−0.841034	−	0.540982i	$-0.818053\pi$
$43$	0.374544	−	6.43067i	0.0571174	−	0.980669i	0.898151	−	0.439686i	$-0.144910\pi$
$44$	−0.879381	−	4.98722i	−0.132572	−	0.751852i
$45$	−5.58716	−	3.52957i	−0.832885	−	0.526158i
$46$	−0.526208	+	2.98428i	−0.0775852	+	0.440007i
$47$	11.1130	+	2.63384i	1.62100	+	0.384185i	0.938111	−	0.346335i	$-0.112574\pi$
$47$	11.1130	+	2.63384i	1.62100	+	0.384185i	0.682892	+	0.730520i	$0.260722\pi$
$48$	0.700595	+	1.58403i	0.101122	+	0.228636i
$49$	0.376098	+	6.45735i	0.0537283	+	0.922479i
$50$	0.143333	−	0.0339705i	0.0202703	−	0.00480416i
$51$	0.487382	−	0.0615053i	0.0682471	−	0.00861246i
$52$	−3.01790	+	0.352742i	−0.418508	+	0.0489166i
$53$	4.27064	+	7.39697i	0.586618	+	1.01605i	0.994672	+	0.103094i	$0.0328743\pi$
$53$	4.27064	+	7.39697i	0.586618	+	1.01605i	−0.408054	+	0.912958i	$0.633792\pi$
$54$	−4.57750	+	2.45896i	−0.622919	+	0.334622i
$55$	5.57787	−	9.66116i	0.752120	−	1.30271i
$56$	−0.288813	+	0.669545i	−0.0385943	+	0.0894717i
$57$	0.276897	+	0.894926i	0.0366758	+	0.118536i
$58$	5.41577	+	5.74038i	0.711125	+	0.753749i
$59$	−9.12046	−	4.58047i	−1.18738	−	0.596326i	−0.258252	−	0.966078i	$-0.583146\pi$
$59$	−9.12046	−	4.58047i	−1.18738	−	0.596326i	−0.929131	+	0.369752i	$0.879443\pi$
$60$	−1.06071	+	3.66510i	−0.136937	+	0.473163i
$61$	3.98650	+	13.3158i	0.510419	+	1.70492i	0.692310	+	0.721600i	$0.256593\pi$
$61$	3.98650	+	13.3158i	0.510419	+	1.70492i	−0.181891	+	0.983319i	$0.558222\pi$
$62$	4.82873	+	4.05179i	0.613250	+	0.514578i
$63$	−2.06900	−	0.710332i	−0.260669	−	0.0894935i
$64$	0.766044	−	0.642788i	0.0957556	−	0.0803485i
$65$	−5.59221	−	3.67806i	−0.693629	−	0.456207i
$66$	−4.45521	−	7.55567i	−0.548398	−	0.930039i
$67$	−11.1908	−	1.30802i	−1.36718	−	0.159800i	−0.599365	−	0.800476i	$-0.704580\pi$
$67$	−11.1908	−	1.30802i	−1.36718	−	0.159800i	−0.767812	+	0.640676i	$0.778654\pi$
$68$	−0.112337	−	0.260426i	−0.0136228	−	0.0315813i
$69$	0.958813	+	5.16034i	0.115427	+	0.621231i
$70$	−1.43544	+	0.720905i	−0.171568	+	0.0861647i
$71$	12.5701	+	4.57514i	1.49180	+	0.542969i	0.953922	−	0.300056i	$-0.0970054\pi$
$71$	12.5701	+	4.57514i	1.49180	+	0.542969i	0.537874	+	0.843025i	$0.319228\pi$
$72$	2.09842	+	2.14397i	0.247302	+	0.252670i
$73$	9.45983	−	3.44310i	1.10719	−	0.402984i	0.277227	−	0.960804i	$-0.410584\pi$
$73$	9.45983	−	3.44310i	1.10719	−	0.402984i	0.829962	+	0.557820i	$0.188362\pi$
$74$	−2.98879	+	3.16793i	−0.347439	+	0.368264i
$75$	0.211868	−	0.142150i	0.0244645	−	0.0164141i
$76$	0.451876	−	0.297203i	0.0518337	−	0.0340916i
$77$	1.05907	−	3.53755i	0.120693	−	0.403141i
$78$	−4.68109	+	2.40497i	−0.530029	+	0.272310i
$79$	−4.78134	−	6.42245i	−0.537942	−	0.722582i	0.447179	−	0.894445i	$-0.352429\pi$
$79$	−4.78134	−	6.42245i	−0.537942	−	0.722582i	−0.985121	+	0.171863i	$0.945021\pi$
$80$	2.20288			0.246290
$81$	−5.93178	+	6.76860i	−0.659087	+	0.752067i
$82$	−4.77300			−0.527090
$83$	8.80861	+	11.8320i	0.966871	+	1.29873i	0.954312	+	0.298812i	$0.0965904\pi$
$83$	8.80861	+	11.8320i	0.966871	+	1.29873i	0.0125591	+	0.999921i	$0.496002\pi$
$84$	−0.0618626	+	1.26146i	−0.00674976	+	0.137637i
$85$	0.179191	−	0.598538i	0.0194359	−	0.0649206i
$86$	−5.38186	+	3.53970i	−0.580340	+	0.381696i
$87$	12.2710	+	6.02238i	1.31559	+	0.645667i
$88$	−3.47523	+	3.68353i	−0.370461	+	0.392666i
$89$	−3.62265	+	1.31854i	−0.384000	+	0.139765i	−0.526805	−	0.849986i	$-0.676610\pi$
$89$	−3.62265	+	1.31854i	−0.384000	+	0.139765i	0.142805	+	0.989751i	$0.454388\pi$
$90$	0.505270	+	6.58931i	0.0532601	+	0.694574i
$91$	−2.08196	−	0.757772i	−0.218249	−	0.0794361i
$92$	2.70799	−	1.36000i	0.282327	−	0.141790i
$93$	10.2933	+	3.63985i	1.06737	+	0.377434i
$94$	−4.52358	−	10.4868i	−0.466572	−	1.08164i
$95$	1.18338	+	0.138317i	0.121412	+	0.0141910i
$96$	0.852224	−	1.50788i	0.0869798	−	0.153898i
$97$	−12.3125	−	8.09807i	−1.25015	−	0.822234i	−0.260460	−	0.965485i	$-0.583874\pi$
$97$	−12.3125	−	8.09807i	−1.25015	−	0.822234i	−0.989686	+	0.143250i	$0.954245\pi$
$98$	4.95500	−	4.15774i	0.500531	−	0.419995i
$99$	−11.8154	−	9.55030i	−1.18749	−	0.959842i
$100$	−0.112841	−	0.0946849i	−0.0112841	−	0.00946849i
$101$	3.53288	+	11.8007i	0.351535	+	1.17421i	0.932770	+	0.360473i	$0.117385\pi$
$101$	3.53288	+	11.8007i	0.351535	+	1.17421i	−0.581235	+	0.813736i	$0.697430\pi$
$102$	−0.340379	−	0.354212i	−0.0337025	−	0.0350722i
$103$	5.51008	+	2.76727i	0.542924	+	0.272667i	0.699053	−	0.715070i	$-0.253605\pi$
$103$	5.51008	+	2.76727i	0.542924	+	0.272667i	−0.156129	+	0.987737i	$0.549901\pi$
$104$	2.08511	+	2.21009i	0.204462	+	0.216717i
$105$	−1.89060	+	2.04113i	−0.184504	+	0.199194i
$106$	3.38303	−	7.84275i	0.328589	−	0.761755i
$107$	−3.19249	+	5.52955i	−0.308630	+	0.534562i	−0.978063	−	0.208310i	$-0.933204\pi$
$107$	−3.19249	+	5.52955i	−0.308630	+	0.534562i	0.669433	+	0.742872i	$0.266537\pi$
$108$	4.70588	+	2.20333i	0.452824	+	0.212016i
$109$	−4.62539	−	8.01141i	−0.443032	−	0.767354i	0.554881	−	0.831930i	$-0.312764\pi$
$109$	−4.62539	−	8.01141i	−0.443032	−	0.767354i	−0.997913	+	0.0645758i	$0.979431\pi$
$110$	−11.0803	+	1.29510i	−1.05647	+	0.123483i
$111$	−2.92418	+	6.95377i	−0.277551	+	0.660023i
$112$	0.709525	−	0.168160i	0.0670438	−	0.0158897i
$113$	−0.175582	−	3.01463i	−0.0165174	−	0.283593i	−0.996445	−	0.0842410i	$-0.973153\pi$
$113$	−0.175582	−	3.01463i	−0.0165174	−	0.283593i	0.979928	−	0.199352i	$-0.0638836\pi$
$114$	0.552490	−	0.756518i	0.0517454	−	0.0708544i
$115$	6.49549	+	1.53946i	0.605708	+	0.143555i
$116$	1.37042	−	7.77203i	0.127240	−	0.721615i
$117$	−6.13260	+	6.74395i	−0.566959	+	0.623478i
$118$	1.77226	+	10.0510i	0.163150	+	0.925269i
$119$	0.0120250	−	0.206461i	0.00110233	−	0.0189263i
$120$	3.57328	−	1.33783i	0.326194	−	0.122126i
$121$	8.74579	−	11.7476i	0.795072	−	1.06797i
$122$	8.30037	−	11.1493i	0.751480	−	1.00941i
$123$	−7.74224	+	2.89868i	−0.698095	+	0.261365i
$124$	0.366514	−	6.29280i	0.0329139	−	0.565110i
$125$	−1.96898	−	11.1666i	−0.176111	−	0.998775i
$126$	0.665747	+	2.08377i	0.0593094	+	0.185637i
$127$	−1.81539	+	10.2956i	−0.161089	+	0.913584i	0.791916	+	0.610630i	$0.209084\pi$
$127$	−1.81539	+	10.2956i	−0.161089	+	0.913584i	−0.953005	+	0.302953i	$0.902027\pi$
$128$	−0.973045	−	0.230616i	−0.0860058	−	0.0203838i
$129$	−6.58017	+	9.01015i	−0.579352	+	0.793300i
$130$	0.389184	+	6.68203i	0.0341337	+	0.586053i
$131$	6.68059	−	1.58333i	0.583686	−	0.138336i	0.0718440	−	0.997416i	$-0.477112\pi$
$131$	6.68059	−	1.58333i	0.583686	−	0.138336i	0.511842	+	0.859080i	$0.328963\pi$
$132$	−3.40011	+	8.08556i	−0.295942	+	0.703757i
$133$	0.391712	−	0.0457846i	0.0339658	−	0.00397003i
$134$	5.63350	+	9.75752i	0.486661	+	0.842921i
$135$	4.82132	+	10.3816i	0.414954	+	0.893506i
$136$	−0.141811	+	0.245624i	−0.0121602	+	0.0210621i
$137$	2.98704	−	6.92473i	0.255200	−	0.591620i	−0.741663	−	0.670773i	$-0.765962\pi$
$137$	2.98704	−	6.92473i	0.255200	−	0.591620i	0.996862	+	0.0791533i	$0.0252217\pi$
$138$	3.56666	−	3.85062i	0.303614	−	0.327787i
$139$	2.46886	+	2.61683i	0.209406	+	0.221957i	0.823560	−	0.567229i	$-0.191984\pi$
$139$	2.46886	+	2.61683i	0.209406	+	0.221957i	−0.614155	+	0.789186i	$0.710503\pi$
$140$	1.43544	+	0.720905i	0.121317	+	0.0609276i
$141$	−13.7064	−	14.2634i	−1.15429	−	1.20120i
$142$	−3.83651	−	12.8148i	−0.321953	−	1.07540i
$143$	−11.7873	−	9.89069i	−0.985701	−	0.827101i
$144$	0.466638	−	2.96349i	0.0388865	−	0.246957i
$145$	13.3177	−	11.1749i	1.10597	−	0.928021i
$146$	−8.41080	−	5.53187i	−0.696083	−	0.457821i
$147$	5.51244	−	9.75344i	0.454658	−	0.804450i
$148$	4.32585	+	0.505619i	0.355582	+	0.0415616i
$149$	−4.55919	−	10.5694i	−0.373504	−	0.865879i	−0.996495	−	0.0836502i	$-0.973342\pi$
$149$	−4.55919	−	10.5694i	−0.373504	−	0.865879i	0.622992	−	0.782229i	$-0.285917\pi$
$150$	−0.240541	−	0.0850583i	−0.0196401	−	0.00694498i
$151$	−12.5774	+	6.31660i	−1.02353	+	0.514038i	−0.879682	−	0.475562i	$-0.842245\pi$
$151$	−12.5774	+	6.31660i	−1.02353	+	0.514038i	−0.143851	+	0.989599i	$0.545949\pi$
$152$	−0.508235	−	0.184983i	−0.0412233	−	0.0150041i
$153$	−0.767241	−	0.367849i	−0.0620278	−	0.0297389i
$154$	−3.46998	+	1.26297i	−0.279619	+	0.101773i
$155$	9.52901	−	10.1002i	0.765389	−	0.811265i
$156$	4.72444	+	2.31866i	0.378258	+	0.185642i
$157$	5.96027	−	3.92013i	0.475682	−	0.312861i	−0.288932	−	0.957350i	$-0.593300\pi$
$157$	5.96027	−	3.92013i	0.475682	−	0.312861i	0.764614	+	0.644489i	$0.222930\pi$
$158$	−2.29638	+	7.67044i	−0.182690	+	0.610228i
$159$	0.724631	−	14.7762i	0.0574670	−	1.17183i
$160$	−1.31547	−	1.76698i	−0.103997	−	0.139692i
$161$	2.20964			0.174144
$162$	8.97147	+	0.716088i	0.704865	+	0.0562612i
$163$	−12.3596			−0.968076			−0.484038	−	0.875047i	$-0.660830\pi$
$163$	−12.3596			−0.968076			−0.484038	+	0.875047i	$0.660830\pi$
$164$	2.85024	+	3.82854i	0.222566	+	0.298958i
$165$	−17.1868	+	8.82992i	−1.33799	+	0.687409i
$166$	4.23060	−	14.1312i	0.328358	−	1.09679i
$167$	−2.18735	+	1.43864i	−0.169262	+	0.111326i	−0.631314	−	0.775528i	$-0.717484\pi$
$167$	−2.18735	+	1.43864i	−0.169262	+	0.111326i	0.462051	+	0.886853i	$0.347114\pi$
$168$	1.04879	−	0.703671i	0.0809158	−	0.0542894i
$169$	2.58564	−	2.74061i	0.198895	−	0.210817i
$170$	−0.587107	+	0.213689i	−0.0450290	+	0.0163892i
$171$	0.436751	−	1.56267i	0.0333991	−	0.119501i
$172$	6.05310	+	2.20315i	0.461544	+	0.167988i
$173$	1.01777	−	0.511142i	0.0773794	−	0.0388614i	−0.409689	−	0.912225i	$-0.634363\pi$
$173$	1.01777	−	0.511142i	0.0773794	−	0.0388614i	0.487068	+	0.873364i	$0.338066\pi$
$174$	−2.49706	−	13.4392i	−0.189302	−	1.01882i
$175$	−0.0425432	−	0.0986263i	−0.00321597	−	0.00745544i
$176$	5.02991	+	0.587913i	0.379144	+	0.0443156i
$177$	8.97881	+	15.2273i	0.674888	+	1.14456i
$178$	3.22092	+	2.11843i	0.241418	+	0.158783i
$179$	−15.3658	+	12.8934i	−1.14849	+	0.963701i	−0.999683	−	0.0251652i	$-0.991989\pi$
$179$	−15.3658	+	12.8934i	−1.14849	+	0.963701i	−0.148810	+	0.988866i	$0.547544\pi$
$180$	4.98371	−	4.34015i	0.371464	−	0.323496i
$181$	13.5059	+	11.3328i	1.00389	+	0.842360i	0.987518	−	0.157506i	$-0.0503454\pi$
$181$	13.5059	+	11.3328i	1.00389	+	0.842360i	0.0163675	+	0.999866i	$0.494790\pi$
$182$	0.635434	+	2.12250i	0.0471015	+	0.157330i
$183$	6.69289	−	23.1261i	0.494753	−	1.70953i
$184$	−2.70799	−	1.36000i	−0.199635	−	0.100261i
$185$	6.58395	+	6.97858i	0.484061	+	0.513075i
$186$	−3.22714	−	10.4301i	−0.236625	−	0.764770i
$187$	0.568891	−	1.31884i	0.0416014	−	0.0964430i
$188$	−5.71044	+	9.89078i	−0.416477	+	0.721359i
$189$	2.34539	+	2.97576i	0.170602	+	0.216454i
$190$	−0.595718	−	1.03181i	−0.0432179	−	0.0748556i
$191$	8.85834	−	1.03539i	0.640967	−	0.0749183i	0.210600	−	0.977572i	$-0.432458\pi$
$191$	8.85834	−	1.03539i	0.640967	−	0.0749183i	0.430367	+	0.902654i	$0.358384\pi$
$192$	−1.71842	+	0.216857i	−0.124016	+	0.0156503i
$193$	−25.2513	+	5.98466i	−1.81763	+	0.430786i	−0.991213	−	0.132277i	$-0.957771\pi$
$193$	−25.2513	+	5.98466i	−1.81763	+	0.430786i	−0.826415	+	0.563062i	$0.809623\pi$
$194$	0.856876	+	14.7120i	0.0615201	+	1.05626i
$195$	4.68933	+	10.6025i	0.335810	+	0.759261i
$196$	−6.29394	−	1.49169i	−0.449567	−	0.106549i
$197$	0.832438	−	4.72099i	0.0593087	−	0.336357i	−0.940687	−	0.339276i	$-0.889818\pi$
$197$	0.832438	−	4.72099i	0.0593087	−	0.336357i	0.999996	+	0.00291905i	$0.000929164\pi$
$198$	−0.604876	+	15.1804i	−0.0429867	+	1.07883i
$199$	1.77930	+	10.0909i	0.126131	+	0.715325i	0.980630	+	0.195871i	$0.0627535\pi$
$199$	1.77930	+	10.0909i	0.126131	+	0.715325i	−0.854498	+	0.519454i	$0.826135\pi$
$200$	−0.00856494	+	0.147054i	−0.000605632	+	0.0103983i
$201$	15.0639	+	12.4063i	1.06252	+	0.875074i
$202$	7.35588	−	9.88067i	0.517558	−	0.695201i
$203$	3.43643	−	4.61592i	0.241190	−	0.323974i
$204$	−0.0808613	+	0.484547i	−0.00566142	+	0.0339250i
$205$	−0.611356	+	10.4966i	−0.0426990	+	0.733113i
$206$	−1.07070	−	6.07226i	−0.0745994	−	0.423074i
$207$	3.44694	−	8.41212i	0.239579	−	0.584683i
$208$	0.527621	−	2.99229i	0.0365840	−	0.207478i
$209$	2.66513	+	0.631648i	0.184351	+	0.0436920i
$210$	2.76623	+	0.297621i	0.190888	+	0.0205378i
$211$	0.900265	+	15.4570i	0.0619768	+	1.06410i	0.875702	+	0.482851i	$0.160399\pi$
$211$	0.900265	+	15.4570i	0.0619768	+	1.06410i	−0.813726	+	0.581249i	$0.802564\pi$
$212$	−8.31106	+	1.96976i	−0.570806	+	0.135283i
$213$	−14.0057	−	18.4569i	−0.959656	−	1.26465i
$214$	6.34180	−	0.741251i	0.433517	−	0.0506709i
$215$	7.09502	+	12.2889i	0.483876	+	0.838098i
$216$	−1.04282	−	5.09044i	−0.0709547	−	0.346360i
$217$	2.29818	−	3.98056i	0.156011	−	0.270218i
$218$	−3.66405	+	8.49422i	−0.248161	+	0.575301i
$219$	−17.0026	−	3.86526i	−1.14893	−	0.261190i
$220$	7.65554	+	8.11439i	0.516136	+	0.547072i
$221$	−0.770106	−	0.386762i	−0.0518030	−	0.0260164i
$222$	7.32398	−	1.80696i	0.491553	−	0.121275i
$223$	5.79877	+	19.3692i	0.388314	+	1.29706i	0.899248	+	0.437439i	$0.144114\pi$
$223$	5.79877	+	19.3692i	0.388314	+	1.29706i	−0.510934	+	0.859620i	$0.670700\pi$
$224$	−0.558584	−	0.468708i	−0.0373220	−	0.0313169i
$225$	−0.441836	+	0.00810988i	−0.0294557	+	0.000540659i
$226$	−2.31326	+	1.94105i	−0.153875	+	0.129117i
$227$	−11.5338	−	7.58589i	−0.765525	−	0.503493i	0.105688	−	0.994399i	$-0.466296\pi$
$227$	−11.5338	−	7.58589i	−0.765525	−	0.503493i	−0.871213	+	0.490906i	$0.836666\pi$
$228$	−0.936745	+	0.00859623i	−0.0620374	+	0.000569299i
$229$	3.90543	+	0.456479i	0.258078	+	0.0301650i	0.244148	−	0.969738i	$-0.421492\pi$
$229$	3.90543	+	0.456479i	0.258078	+	0.0301650i	0.0139299	+	0.999903i	$0.495566\pi$
$230$	−2.64400	−	6.12948i	−0.174340	−	0.404166i
$231$	−4.86162	+	4.15600i	−0.319871	+	0.273445i
$232$	−7.05248	+	3.54189i	−0.463018	+	0.232536i
$233$	−3.72397	−	1.35542i	−0.243966	−	0.0887962i	0.217143	−	0.976140i	$-0.430326\pi$
$233$	−3.72397	−	1.35542i	−0.243966	−	0.0887962i	−0.461109	+	0.887343i	$0.652548\pi$
$234$	9.07161	+	0.891897i	0.593030	+	0.0583051i
$235$	−23.6416	+	8.60485i	−1.54221	+	0.561318i
$236$	7.00382	−	7.42361i	0.455910	−	0.483236i
$237$	0.933374	+	13.8368i	0.0606292	+	0.898794i
$238$	−0.172788	+	0.113645i	−0.0112002	+	0.00736649i
$239$	−0.367489	+	1.22750i	−0.0237709	+	0.0794004i	−0.969052	−	0.246857i	$-0.920602\pi$
$239$	−0.367489	+	1.22750i	−0.0237709	+	0.0794004i	0.945281	+	0.326257i	$0.105787\pi$
$240$	−3.20691	−	2.06731i	−0.207005	−	0.133445i
$241$	10.6032	+	14.2426i	0.683015	+	0.917449i	0.999515	−	0.0311439i	$-0.00991502\pi$
$241$	10.6032	+	14.2426i	0.683015	+	0.917449i	−0.316500	+	0.948593i	$0.602508\pi$
$242$	−14.6457			−0.941459
$243$	14.9874	−	4.28687i	0.961443	−	0.275003i
$244$	−13.8998			−0.889842
$245$	−8.50886	−	11.4294i	−0.543611	−	0.730196i
$246$	6.94844	+	4.47926i	0.443017	+	0.285587i
$247$	0.471319	−	1.57432i	0.0299893	−	0.100171i
$248$	−5.26647	+	3.46381i	−0.334421	+	0.219952i
$249$	−1.71955	−	25.4913i	−0.108972	−	1.61545i
$250$	−7.78123	+	8.24762i	−0.492128	+	0.521626i
$251$	−10.0584	+	3.66094i	−0.634878	+	0.231077i	−0.639353	−	0.768913i	$-0.720798\pi$
$251$	−10.0584	+	3.66094i	−0.634878	+	0.231077i	0.00447526	+	0.999990i	$0.498575\pi$
$252$	1.27389	−	1.77835i	0.0802473	−	0.112026i
$253$	14.4205	+	5.24863i	0.906609	+	0.329979i
$254$	9.34238	−	4.69192i	0.586193	−	0.294397i
$255$	−0.822565	+	0.703177i	−0.0515110	+	0.0440347i
$256$	0.396080	+	0.918216i	0.0247550	+	0.0573885i
$257$	−9.55827	−	1.11720i	−0.596228	−	0.0696891i	−0.187374	−	0.982289i	$-0.559998\pi$
$257$	−9.55827	−	1.11720i	−0.596228	−	0.0696891i	−0.408854	+	0.912600i	$0.634072\pi$
$258$	11.1567	−	0.102381i	0.694583	−	0.00637399i
$259$	2.65334	+	1.74513i	0.164870	+	0.108437i
$260$	5.12740	−	4.30240i	0.317988	−	0.266824i
$261$	−12.2122	−	20.2831i	−0.755915	−	1.25549i
$262$	−5.25939	−	4.41316i	−0.324926	−	0.272646i
$263$	4.55233	+	15.2058i	0.280709	+	0.937633i	0.975792	+	0.218703i	$0.0701825\pi$
$263$	4.55233	+	15.2058i	0.280709	+	0.937633i	−0.695083	+	0.718930i	$0.744632\pi$
$264$	8.51602	−	2.10105i	0.524125	−	0.129311i
$265$	−16.8141	−	8.44436i	−1.03288	−	0.518733i
$266$	−0.270639	−	0.286861i	−0.0165940	−	0.0175886i
$267$	6.51117	+	1.48020i	0.398477	+	0.0905871i
$268$	4.46263	−	10.3455i	0.272599	−	0.631955i
$269$	−2.28016	+	3.94936i	−0.139024	+	0.240797i	−0.927127	−	0.374746i	$-0.877730\pi$
$269$	−2.28016	+	3.94936i	−0.139024	+	0.240797i	0.788103	+	0.615543i	$0.211063\pi$
$270$	5.44823	−	10.0668i	0.331569	−	0.612643i
$271$	−0.0681966	−	0.118120i	−0.00414265	−	0.00717528i	0.863947	−	0.503583i	$-0.167985\pi$
$271$	−0.0681966	−	0.118120i	−0.00414265	−	0.00717528i	−0.868089	+	0.496408i	$0.834652\pi$
$272$	0.281704	−	0.0329265i	0.0170808	−	0.00199646i
$273$	2.31974	+	3.05698i	0.140397	+	0.185017i
$274$	−7.33823	+	1.73919i	−0.443318	+	0.105068i
$275$	−0.0433742	−	0.744706i	−0.00261556	−	0.0449074i
$276$	−5.21854	−	0.561468i	−0.314119	−	0.0337964i
$277$	13.1587	+	3.11867i	0.790630	+	0.187383i	0.606041	−	0.795433i	$-0.292757\pi$
$277$	13.1587	+	3.11867i	0.790630	+	0.187383i	0.184589	+	0.982816i	$0.440905\pi$
$278$	0.624725	−	3.54299i	0.0374685	−	0.212494i
$279$	−11.5690	−	14.9587i	−0.692616	−	0.895552i
$280$	−0.278931	−	1.58190i	−0.0166693	−	0.0945363i
$281$	0.0935867	−	1.60682i	0.00558292	−	0.0958550i	−0.994366	−	0.106005i	$-0.966194\pi$
$281$	0.0935867	−	1.60682i	0.00558292	−	0.0958550i	0.999948	+	0.0101503i	$0.00323100\pi$
$282$	−3.25612	+	19.5117i	−0.193899	+	1.16191i
$283$	0.910877	−	1.22352i	0.0541460	−	0.0727307i	−0.774225	−	0.632910i	$-0.781860\pi$
$283$	0.910877	−	1.22352i	0.0541460	−	0.0727307i	0.828371	+	0.560179i	$0.189268\pi$
$284$	−7.98808	+	10.7299i	−0.474005	+	0.636700i
$285$	−1.59294	−	1.31191i	−0.0943574	−	0.0777109i
$286$	−0.894685	+	15.3611i	−0.0529038	+	0.908324i
$287$	0.604361	+	3.42750i	0.0356743	+	0.202319i
$288$	−2.65574	+	1.39537i	−0.156491	+	0.0822230i
$289$	−2.93805	+	16.6625i	−0.172827	+	0.980148i
$290$	−16.9164	−	4.00925i	−0.993364	−	0.235432i
$291$	10.3246	+	23.3438i	0.605240	+	1.36844i
$292$	0.585340	+	10.0499i	0.0342545	+	0.588126i
$293$	19.0936	−	4.52526i	1.11546	−	0.264369i	0.368756	−	0.929526i	$-0.379784\pi$
$293$	19.0936	−	4.52526i	1.11546	−	0.264369i	0.746703	+	0.665158i	$0.231636\pi$
$294$	−11.1153	+	1.40269i	−0.648255	+	0.0818068i
$295$	22.3307	−	2.61009i	1.30014	−	0.151965i
$296$	−2.17765	−	3.77180i	−0.126573	−	0.219231i
$297$	8.23801	+	24.9914i	0.478018	+	1.45015i
$298$	−5.75540	+	9.96864i	−0.333401	+	0.577468i
$299$	3.64689	−	8.45443i	0.210905	−	0.488932i
$300$	0.0754139	+	0.243737i	0.00435403	+	0.0140722i
$301$	3.22332	+	3.41652i	0.185789	+	0.196925i
$302$	12.5774	+	6.31660i	0.723747	+	0.363480i
$303$	5.93132	−	20.4946i	0.340745	−	1.17739i
$304$	0.155118	+	0.518131i	0.00889664	+	0.0297169i
$305$	−23.4560	−	19.6819i	−1.34308	−	1.12698i
$306$	0.163104	+	0.835086i	0.00932404	+	0.0477387i
$307$	−11.3654	+	9.53673i	−0.648660	+	0.544290i	−0.906664	−	0.421854i	$-0.861380\pi$
$307$	−11.3654	+	9.53673i	−0.648660	+	0.544290i	0.258004	+	0.966144i	$0.416935\pi$
$308$	3.08519	+	2.02916i	0.175795	+	0.115622i
$309$	−5.42450	−	9.19951i	−0.308589	−	0.523342i
$310$	−13.7919	−	1.61204i	−0.783328	−	0.0915579i
$311$	−1.11210	−	2.57813i	−0.0630613	−	0.146192i	0.883771	−	0.467919i	$-0.154996\pi$
$311$	−1.11210	−	2.57813i	−0.0630613	−	0.146192i	−0.946833	+	0.321727i	$0.895737\pi$
$312$	−0.961387	−	5.17419i	−0.0544278	−	0.292931i
$313$	22.4726	−	11.2862i	1.27023	−	0.637932i	0.319390	−	0.947623i	$-0.396522\pi$
$313$	22.4726	−	11.2862i	1.27023	−	0.637932i	0.950837	+	0.309691i	$0.100226\pi$
$314$	−6.70366	−	2.43993i	−0.378309	−	0.137693i
$315$	4.66782	−	1.19718i	0.263002	−	0.0674534i
$316$	7.52394	−	2.73849i	0.423255	−	0.154052i
$317$	12.0580	−	12.7807i	0.677244	−	0.717837i	−0.294031	−	0.955796i	$-0.594997\pi$
$317$	12.0580	−	12.7807i	0.677244	−	0.717837i	0.971275	+	0.237959i	$0.0764783\pi$
$318$	−12.2850	+	8.24248i	−0.688911	+	0.462216i
$319$	33.3910	−	21.9616i	1.86954	−	1.22962i
$320$	−0.631794	+	2.11034i	−0.0353184	+	0.117972i
$321$	9.83682	−	5.05380i	0.549038	−	0.282075i
$322$	−1.31951	−	1.77241i	−0.0735333	−	0.0987723i
$323$	0.153398			0.00853527
$324$	−4.78300	−	7.62384i	−0.265722	−	0.423547i
$325$	−0.447574			−0.0248270
$326$	7.38062	+	9.91390i	0.408775	+	0.549080i
$327$	−0.784823	+	16.0036i	−0.0434008	+	0.885001i
$328$	1.36891	−	4.57249i	0.0755856	−	0.252473i
$329$	−6.95784	+	4.57625i	−0.383598	+	0.252297i
$330$	17.3459	+	8.51303i	0.954860	+	0.468627i
$331$	9.84380	−	10.4338i	0.541064	−	0.573494i	−0.397935	−	0.917413i	$-0.630273\pi$
$331$	9.84380	−	10.4338i	0.541064	−	0.573494i	0.938999	+	0.343919i	$0.111755\pi$
$332$	−13.8613	+	5.04510i	−0.760737	+	0.276886i
$333$	10.7828	−	7.37895i	0.590893	−	0.404364i
$334$	2.46017	+	0.895427i	0.134614	+	0.0489956i
$335$	22.1799	−	11.1392i	1.21182	−	0.608597i
$336$	−1.19072	−	0.421055i	−0.0649593	−	0.0229704i
$337$	−4.67503	−	10.8379i	−0.254665	−	0.590380i	0.742141	−	0.670244i	$-0.233811\pi$
$337$	−4.67503	−	10.8379i	−0.254665	−	0.590380i	−0.996806	+	0.0798642i	$0.974551\pi$
$338$	−3.74235	−	0.437417i	−0.203557	−	0.0237924i
$339$	−2.57350	+	4.55342i	−0.139773	+	0.247308i
$340$	0.522001	+	0.343325i	0.0283095	+	0.0186194i
$341$	24.4535	−	20.5189i	1.32423	−	1.11116i
$342$	−1.51426	+	0.582835i	−0.0818821	+	0.0315161i
$343$	−7.52318	−	6.31270i	−0.406213	−	0.340854i
$344$	−1.84746	−	6.17096i	−0.0996086	−	0.332716i
$345$	−8.01129	−	8.33686i	−0.431313	−	0.448841i
$346$	−1.01777	−	0.511142i	−0.0547155	−	0.0274792i
$347$	20.3266	+	21.5449i	1.09119	+	1.15659i	0.986781	+	0.162058i	$0.0518131\pi$
$347$	20.3266	+	21.5449i	1.09119	+	1.15659i	0.104407	+	0.994535i	$0.466705\pi$
$348$	−9.28875	+	10.0283i	−0.497929	+	0.537572i
$349$	−3.87195	+	8.97620i	−0.207261	+	0.480485i	−0.989861	−	0.142040i	$-0.954634\pi$
$349$	−3.87195	+	8.97620i	−0.207261	+	0.480485i	0.782600	+	0.622525i	$0.213893\pi$
$350$	−0.0537054	+	0.0930204i	−0.00287067	+	0.00497215i
$351$	15.2566	−	4.06251i	0.814339	−	0.216841i
$352$	−2.53208	−	4.38569i	−0.134960	−	0.233758i
$353$	−32.0664	+	3.74803i	−1.70672	+	0.199487i	−0.912765	−	0.408485i	$-0.866057\pi$
$353$	−32.0664	+	3.74803i	−1.70672	+	0.199487i	−0.793958	+	0.607972i	$0.791983\pi$
$354$	6.85242	−	16.2952i	0.364202	−	0.866082i
$355$	−28.6733	+	6.79569i	−1.52182	+	0.360678i
$356$	−0.224156	−	3.84862i	−0.0118803	−	0.203976i
$357$	−0.211261	+	0.289277i	−0.0111811	+	0.0153102i
$358$	19.5179	+	4.62584i	1.03156	+	0.244483i
$359$	−4.20850	+	23.8676i	−0.222116	+	1.25968i	0.646006	+	0.763333i	$0.276438\pi$
$359$	−4.20850	+	23.8676i	−0.222116	+	1.25968i	−0.868122	+	0.496351i	$0.834673\pi$
$360$	−6.45740	−	1.40579i	−0.340335	−	0.0740917i
$361$	−3.24852	−	18.4233i	−0.170975	−	0.969646i
$362$	1.02513	−	17.6009i	0.0538798	−	0.925081i
$363$	−23.7566	+	8.89441i	−1.24690	+	0.466836i
$364$	1.32305	−	1.77717i	0.0693467	−	0.0931488i
$365$	−13.2428	+	17.7881i	−0.693158	+	0.931073i
$366$	−22.5467	+	8.44143i	−1.17853	+	0.441240i
$367$	0.527677	−	9.05987i	0.0275445	−	0.472921i	−0.956128	−	0.292951i	$-0.905363\pi$
$367$	0.527677	−	9.05987i	0.0275445	−	0.472921i	0.983672	−	0.179970i	$-0.0576002\pi$
$368$	0.526208	+	2.98428i	0.0274305	+	0.155566i
$369$	13.9913	+	3.04594i	0.728358	+	0.158565i
$370$	1.66602	−	9.44845i	0.0866121	−	0.491202i
$371$	−6.06026	−	1.43631i	−0.314633	−	0.0745693i
$372$	−6.43909	+	8.81697i	−0.333851	+	0.457139i
$373$	−0.748238	−	12.8468i	−0.0387423	−	0.665180i	−0.960649	−	0.277767i	$-0.910406\pi$
$373$	−0.748238	−	12.8468i	−0.0387423	−	0.665180i	0.921906	−	0.387413i	$-0.126631\pi$
$374$	−1.39759	+	0.331235i	−0.0722676	+	0.0171277i
$375$	−7.61303	+	18.1040i	−0.393135	+	0.934886i
$376$	11.3437	−	1.32588i	0.585005	−	0.0683772i
$377$	−11.9896	−	20.7666i	−0.617496	−	1.06953i
$378$	0.986353	−	3.65829i	0.0507325	−	0.188162i
$379$	8.97890	−	15.5519i	0.461215	−	0.798848i	−0.537806	−	0.843068i	$-0.680747\pi$
$379$	8.97890	−	15.5519i	0.461215	−	0.798848i	0.999022	+	0.0442199i	$0.0140802\pi$
$380$	−0.471904	+	1.09400i	−0.0242081	+	0.0561208i
$381$	12.3048	−	13.2844i	0.630392	−	0.680581i
$382$	−6.12034	−	6.48719i	−0.313144	−	0.331913i
$383$	−20.1321	−	10.1107i	−1.02870	−	0.516634i	−0.147346	−	0.989085i	$-0.547073\pi$
$383$	−20.1321	−	10.1107i	−1.02870	−	0.516634i	−0.881357	+	0.472451i	$0.843369\pi$
$384$	1.20012	+	1.24889i	0.0612432	+	0.0637321i
$385$	2.33301	+	7.79281i	0.118901	+	0.397158i
$386$	19.8795	+	16.6808i	1.01184	+	0.849033i
$387$	18.0349	−	6.94159i	0.916768	−	0.352861i
$388$	11.2891	−	9.47271i	0.573119	−	0.480904i
$389$	−15.9613	−	10.4979i	−0.809272	−	0.532267i	0.0761270	−	0.997098i	$-0.475745\pi$
$389$	−15.9613	−	10.4979i	−0.809272	−	0.532267i	−0.885399	+	0.464831i	$0.846115\pi$
$390$	5.70424	−	10.0928i	0.288845	−	0.511069i
$391$	0.853651	+	0.0997775i	0.0431710	+	0.00504597i
$392$	2.56196	+	5.93929i	0.129399	+	0.299980i
$393$	−11.2114	−	3.96447i	−0.565538	−	0.199981i
$394$	−4.28391	+	2.15146i	−0.215820	+	0.108389i
$395$	16.5744	+	6.03258i	0.833947	+	0.303532i
$396$	12.5378	−	8.57993i	0.630047	−	0.431158i
$397$	−19.3936	+	7.05869i	−0.973337	+	0.354266i	−0.779246	−	0.626718i	$-0.784398\pi$
$397$	−19.3936	+	7.05869i	−0.973337	+	0.354266i	−0.194091	+	0.980984i	$0.562176\pi$
$398$	7.03163	−	7.45309i	0.352464	−	0.373590i
$399$	−0.613214	−	0.300953i	−0.0306991	−	0.0150665i
$400$	0.123070	−	0.0809446i	0.00615351	−	0.00404723i
$401$	−6.47052	+	21.6130i	−0.323122	+	1.07930i	0.629969	+	0.776620i	$0.283068\pi$
$401$	−6.47052	+	21.6130i	−0.323122	+	1.07930i	−0.953091	+	0.302683i	$0.902118\pi$
$402$	0.955877	−	19.4916i	0.0476748	−	0.972153i
$403$	−11.4372	−	15.3629i	−0.569729	−	0.765279i
$404$	−12.3181			−0.612851
$405$	2.72391	−	19.6379i	0.135352	−	0.975817i
$406$	−5.75463			−0.285598
$407$	13.1709	+	17.6915i	0.652856	+	0.876937i
$408$	0.436953	−	0.224490i	0.0216324	−	0.0111139i
$409$	8.82021	−	29.4616i	0.436131	−	1.45678i	−0.404182	−	0.914679i	$-0.632444\pi$
$409$	8.82021	−	29.4616i	0.436131	−	1.45678i	0.840313	−	0.542102i	$-0.182371\pi$
$410$	8.78463	−	5.77774i	0.433842	−	0.285342i
$411$	−10.8470	+	7.27768i	−0.535045	+	0.358981i
$412$	−4.23132	+	4.48494i	−0.208462	+	0.220957i
$413$	6.99324	−	2.54533i	0.344115	−	0.125247i
$414$	−8.80593	+	2.25850i	−0.432788	+	0.110999i
$415$	−30.5348	−	11.1138i	−1.49890	−	0.545553i
$416$	−2.71526	+	1.36365i	−0.133126	+	0.0668586i
$417$	−1.13832	−	6.12645i	−0.0557438	−	0.300014i
$418$	−1.08485	−	2.51496i	−0.0530616	−	0.123011i
$419$	17.6247	+	2.06003i	0.861024	+	0.100639i	0.535133	−	0.844768i	$-0.320262\pi$
$419$	17.6247	+	2.06003i	0.861024	+	0.100639i	0.325891	+	0.945407i	$0.394336\pi$
$420$	−1.41315	−	2.39658i	−0.0689545	−	0.116941i
$421$	0.653753	+	0.429980i	0.0318620	+	0.0209560i	0.565340	−	0.824858i	$-0.308745\pi$
$421$	0.653753	+	0.429980i	0.0318620	+	0.0209560i	−0.533478	+	0.845814i	$0.679115\pi$
$422$	11.8608	−	9.95238i	0.577374	−	0.484474i
$423$	6.56788	+	33.6273i	0.319341	+	1.63501i
$424$	6.54301	+	5.49023i	0.317756	+	0.266629i
$425$	−0.0119822	−	0.0400233i	−0.000581222	−	0.00194142i
$426$	−6.44108	+	22.2560i	−0.312071	+	1.07831i
$427$	−9.05736	−	4.54878i	−0.438316	−	0.220131i
$428$	−4.38164	−	4.64426i	−0.211794	−	0.224489i
$429$	7.87767	+	25.4605i	0.380337	+	1.22925i
$430$	5.62039	−	13.0295i	0.271039	−	0.628339i
$431$	7.23727	−	12.5353i	0.348607	−	0.603805i	−0.637395	−	0.770537i	$-0.719988\pi$
$431$	7.23727	−	12.5353i	0.348607	−	0.603805i	0.986002	+	0.166732i	$0.0533215\pi$
$432$	−3.46043	+	3.87626i	−0.166490	+	0.186497i
$433$	3.01657	+	5.22485i	0.144967	+	0.251090i	0.929361	−	0.369173i	$-0.120359\pi$
$433$	3.01657	+	5.22485i	0.144967	+	0.251090i	−0.784394	+	0.620263i	$0.787026\pi$
$434$	−4.56528	+	0.533605i	−0.219140	+	0.0256138i
$435$	−29.8747	+	3.77005i	−1.43238	+	0.180760i
$436$	9.00143	−	2.13338i	0.431090	−	0.102170i
$437$	0.0952966	+	1.63618i	0.00455866	+	0.0782691i
$438$	7.05285	+	15.9464i	0.336998	+	0.761948i
$439$	−11.7050	−	2.77414i	−0.558650	−	0.132403i	−0.0584156	−	0.998292i	$-0.518605\pi$
$439$	−11.7050	−	2.77414i	−0.558650	−	0.132403i	−0.500235	+	0.865890i	$0.666753\pi$
$440$	1.93717	−	10.9863i	0.0923512	−	0.523750i
$441$	−17.1781	+	9.02567i	−0.818005	+	0.429794i
$442$	0.149645	+	0.848678i	0.00711788	+	0.0403675i
$443$	−0.271415	+	4.66002i	−0.0128953	+	0.221404i	0.985704	+	0.168488i	$0.0538886\pi$
$443$	−0.271415	+	4.66002i	−0.0128953	+	0.221404i	−0.998599	+	0.0529160i	$0.983148\pi$
$444$	−5.82298	−	4.79570i	−0.276346	−	0.227594i
$445$	5.07133	−	6.81197i	0.240404	−	0.322918i
$446$	12.0737	−	16.2178i	0.571707	−	0.767936i
$447$	−3.28176	+	19.6653i	−0.155222	+	0.930138i
$448$	−0.0423980	+	0.727946i	−0.00200312	+	0.0343922i
$449$	1.46834	+	8.32735i	0.0692951	+	0.392992i	0.999653	+	0.0263395i	$0.00838510\pi$
$449$	1.46834	+	8.32735i	0.0692951	+	0.392992i	−0.930358	+	0.366653i	$0.880504\pi$
$450$	0.270351	+	0.349564i	0.0127445	+	0.0164786i
$451$	−4.19729	+	23.8040i	−0.197643	+	1.12089i
$452$	2.93834	+	0.696400i	0.138208	+	0.0327559i
$453$	24.2378	+	2.60777i	1.13879	+	0.122524i
$454$	0.802681	+	13.7815i	0.0376717	+	0.646798i
$455$	4.74910	−	1.12556i	0.222641	−	0.0527669i
$456$	0.566281	+	0.746252i	0.0265185	+	0.0349464i
$457$	−33.6366	+	3.93155i	−1.57345	+	0.183910i	−0.857591	−	0.514332i	$-0.828040\pi$
$457$	−33.6366	+	3.93155i	−1.57345	+	0.183910i	−0.715861	+	0.698243i	$0.753966\pi$
$458$	−1.96601	−	3.40522i	−0.0918654	−	0.159116i
$459$	0.771723	+	1.25553i	0.0360209	+	0.0586032i
$460$	−3.33771	+	5.78109i	−0.155622	+	0.269545i
$461$	6.12644	−	14.2027i	0.285337	−	0.661485i	−0.713912	−	0.700235i	$-0.753078\pi$
$461$	6.12644	−	14.2027i	0.285337	−	0.661485i	0.999249	+	0.0387504i	$0.0123377\pi$
$462$	6.23678	+	1.41783i	0.290161	+	0.0659633i
$463$	25.2116	+	26.7228i	1.17168	+	1.24191i	0.964637	+	0.263582i	$0.0849039\pi$
$463$	25.2116	+	26.7228i	1.17168	+	1.24191i	0.207047	+	0.978331i	$0.433615\pi$
$464$	7.05248	+	3.54189i	0.327403	+	0.164428i
$465$	−23.3507	+	5.76104i	−1.08286	+	0.267162i
$466$	1.13659	+	3.79648i	0.0526516	+	0.175869i
$467$	−8.62378	−	7.23621i	−0.399061	−	0.334852i	0.421070	−	0.907028i	$-0.361655\pi$
$467$	−8.62378	−	7.23621i	−0.399061	−	0.334852i	−0.820130	+	0.572177i	$0.806099\pi$
$468$	−4.70178	−	7.80915i	−0.217340	−	0.360978i
$469$	6.29357	−	5.28094i	0.290610	−	0.243851i
$470$	21.0199	+	13.8250i	0.969578	+	0.637701i
$471$	−12.3557	+	0.113385i	−0.569322	+	0.00522450i
$472$	−10.1370	−	1.18485i	−0.466595	−	0.0545371i
$473$	12.9206	+	29.9532i	0.594088	+	1.37725i
$474$	10.5414	−	9.01142i	0.484183	−	0.413908i
$475$	0.0711953	−	0.0357556i	0.00326666	−	0.00164058i
$476$	0.194339	+	0.0707336i	0.00890752	+	0.00324207i
$477$	−14.9217	+	20.8308i	−0.683219	+	0.953779i
$478$	1.20406	−	0.438240i	0.0550722	−	0.0200446i
$479$	−5.67177	+	6.01172i	−0.259150	+	0.274683i	−0.843865	−	0.536556i	$-0.819725\pi$
$479$	−5.67177	+	6.01172i	−0.259150	+	0.274683i	0.584715	+	0.811239i	$0.301206\pi$
$480$	0.256796	+	3.80686i	0.0117211	+	0.173758i
$481$	11.0563	−	7.27184i	0.504124	−	0.331568i
$482$	5.09253	−	17.0102i	0.231958	−	0.774794i
$483$	−3.21675	−	2.07366i	−0.146367	−	0.0943547i
$484$	8.74579	+	11.7476i	0.397536	+	0.533983i
$485$	32.4637			1.47410
$486$	−12.3885	−	9.46181i	−0.561952	−	0.429197i
$487$	22.3872			1.01446			0.507231	−	0.861810i	$-0.330669\pi$
$487$	22.3872			1.01446			0.507231	+	0.861810i	$0.330669\pi$
$488$	8.30037	+	11.1493i	0.375740	+	0.504707i
$489$	17.9928	+	11.5989i	0.813663	+	0.524522i
$490$	−4.08663	+	13.6503i	−0.184615	+	0.616658i
$491$	−10.8562	+	7.14024i	−0.489934	+	0.322234i	−0.770325	−	0.637651i	$-0.779906\pi$
$491$	−10.8562	+	7.14024i	−0.489934	+	0.322234i	0.280391	+	0.959886i	$0.409536\pi$
$492$	−0.556401	−	8.24834i	−0.0250845	−	0.371864i
$493$	1.53603	−	1.62810i	0.0691793	−	0.0733258i
$494$	−1.54425	+	0.562060i	−0.0694790	+	0.0252883i
$495$	33.3066	+	3.27462i	1.49702	+	0.147183i
$496$	5.92332	+	2.15591i	0.265965	+	0.0968033i
$497$	−8.71659	+	4.37763i	−0.390992	+	0.196364i
$498$	−19.4204	+	16.6017i	−0.870247	+	0.743938i
$499$	16.6848	+	38.6798i	0.746916	+	1.73155i	0.679329	+	0.733834i	$0.262271\pi$
$499$	16.6848	+	38.6798i	0.746916	+	1.73155i	0.0675872	+	0.997713i	$0.478470\pi$
$500$	11.2622	+	1.31637i	0.503663	+	0.0588697i
$501$	4.53441	−	0.0416109i	0.202582	−	0.00185904i
$502$	8.94296	+	5.88188i	0.399144	+	0.262521i
$503$	−11.8063	+	9.90667i	−0.526417	+	0.441717i	−0.866862	−	0.498548i	$-0.833867\pi$
$503$	−11.8063	+	9.90667i	−0.526417	+	0.441717i	0.340445	+	0.940264i	$0.389422\pi$
$504$	−2.18717	+	0.0401454i	−0.0974243	+	0.00178822i
$505$	−20.7870	−	17.4423i	−0.925007	−	0.776173i
$506$	−4.40128	−	14.7013i	−0.195661	−	0.653552i
$507$	−6.33607	+	1.56322i	−0.281395	+	0.0694251i
$508$	−9.34238	−	4.69192i	−0.414501	−	0.208170i
$509$	21.2736	+	22.5487i	0.942937	+	0.999455i	0.999999	+	0.00108391i	$0.000345018\pi$
$509$	21.2736	+	22.5487i	0.942937	+	0.999455i	−0.0570627	+	0.998371i	$0.518174\pi$
$510$	1.05524	+	0.239890i	0.0467267	+	0.0106225i
$511$	−2.90747	+	6.74027i	−0.128619	+	0.298172i
$512$	0.500000	−	0.866025i	0.0220971	−	0.0382733i
$513$	−2.10232	+	1.86503i	−0.0928195	+	0.0823433i
$514$	4.81167	+	8.33405i	0.212234	+	0.367599i
$515$	−13.4910	+	1.57687i	−0.594484	+	0.0694852i
$516$	−6.74442	−	8.88788i	−0.296906	−	0.391267i
$517$	−56.2781	+	13.3382i	−2.47511	+	0.586612i
$518$	−0.184656	−	3.17042i	−0.00811332	−	0.139300i
$519$	−1.96133	−	0.211022i	−0.0860929	−	0.00926283i
$520$	−6.51293	−	1.54359i	−0.285611	−	0.0676910i
$521$	−4.63731	+	26.2995i	−0.203164	+	1.15220i	0.697138	+	0.716937i	$0.254456\pi$
$521$	−4.63731	+	26.2995i	−0.203164	+	1.15220i	−0.900303	+	0.435265i	$0.856655\pi$
$522$	−8.97696	+	21.9079i	−0.392911	+	0.958883i
$523$	−2.75854	−	15.6445i	−0.120622	−	0.684084i	−0.983812	−	0.179204i	$-0.942648\pi$
$523$	−2.75854	−	15.6445i	−0.120622	−	0.684084i	0.863189	−	0.504880i	$-0.168463\pi$
$524$	−0.399202	+	6.85404i	−0.0174392	+	0.299420i
$525$	−0.0306231	+	0.183503i	−0.00133650	+	0.00800874i
$526$	9.47850	−	12.7318i	0.413282	−	0.555134i
$527$	1.06760	−	1.43404i	0.0465054	−	0.0624676i
$528$	−6.77072	−	5.57624i	−0.294658	−	0.242674i
$529$	0.803399	−	13.7938i	0.0349304	−	0.599732i
$530$	3.26727	+	18.5296i	0.141921	+	0.804875i
$531$	1.21904	−	30.5939i	0.0529017	−	1.32766i
$532$	−0.0684832	+	0.388387i	−0.00296912	+	0.0168387i
$533$	14.1116	+	3.34451i	0.611242	+	0.144867i
$534$	−2.70089	−	6.10668i	−0.116879	−	0.264262i
$535$	−0.817828	−	14.0416i	−0.0353578	−	0.607070i
$536$	−10.9633	+	2.59835i	−0.473543	+	0.112232i
$537$	34.4692	−	4.34985i	1.48745	−	0.187710i
$538$	4.52949	−	0.529421i	0.195280	−	0.0228250i
$539$	−16.3782	−	28.3679i	−0.705460	−	1.22189i
$540$	−11.3282	+	1.64130i	−0.487490	+	0.0706304i
$541$	−20.8927	+	36.1873i	−0.898249	+	1.55581i	−0.0685168	+	0.997650i	$0.521827\pi$
$541$	−20.8927	+	36.1873i	−0.898249	+	1.55581i	−0.829732	+	0.558162i	$0.811507\pi$
$542$	−0.0540226	+	0.125238i	−0.00232047	+	0.00537945i
$543$	−9.02626	−	29.1728i	−0.387354	−	1.25192i
$544$	−0.194633	−	0.206299i	−0.00834482	−	0.00884500i
$545$	18.2108	+	9.14581i	0.780065	+	0.391763i
$546$	1.06682	−	3.68622i	0.0456558	−	0.157756i
$547$	−13.2184	−	44.1524i	−0.565176	−	1.88782i	−0.446225	−	0.894921i	$-0.647232\pi$
$547$	−13.2184	−	44.1524i	−0.565176	−	1.88782i	−0.118952	−	0.992900i	$-0.537953\pi$
$548$	5.77713	+	4.84759i	0.246787	+	0.207079i
$549$	−31.4463	+	27.3855i	−1.34209	+	1.16879i
$550$	−0.571444	+	0.479499i	−0.0243665	+	0.0204459i
$551$	3.56617	+	2.34551i	0.151924	+	0.0999219i
$552$	2.66593	+	4.52120i	0.113469	+	0.192435i
$553$	5.79893	+	0.677798i	0.246596	+	0.0288229i
$554$	−5.35628	−	12.4172i	−0.227566	−	0.527558i
$555$	−3.03568	−	16.3380i	−0.128857	−	0.693511i
$556$	−3.21498	+	1.61462i	−0.136345	+	0.0684752i
$557$	1.38357	+	0.503577i	0.0586236	+	0.0213372i	0.371165	−	0.928567i	$-0.378958\pi$
$557$	1.38357	+	0.503577i	0.0586236	+	0.0213372i	−0.312542	+	0.949904i	$0.601180\pi$
$558$	−5.09019	+	18.2124i	−0.215485	+	0.770994i
$559$	18.3920	−	6.69415i	0.777900	−	0.283133i
$560$	−1.10231	+	1.16838i	−0.0465811	+	0.0493730i
$561$	−2.06586	+	1.38606i	−0.0872205	+	0.0585194i
$562$	−1.34476	+	0.884459i	−0.0567251	+	0.0373087i
$563$	4.39243	−	14.6717i	0.185119	−	0.618339i	−0.814170	−	0.580627i	$-0.802808\pi$
$563$	4.39243	−	14.6717i	0.185119	−	0.618339i	0.999289	−	0.0377128i	$-0.0120072\pi$
$564$	17.5952	−	9.03979i	0.740893	−	0.380644i
$565$	3.97238	+	5.33583i	0.167119	+	0.224480i
$566$	−1.52535			−0.0641153
$567$	−0.621750	−	6.53310i	−0.0261110	−	0.274364i
$568$	13.3768			0.561279
$569$	−5.20132	−	6.98659i	−0.218051	−	0.292893i	0.679616	−	0.733568i	$-0.262146\pi$
$569$	−5.20132	−	6.98659i	−0.218051	−	0.292893i	−0.897667	+	0.440675i	$0.854739\pi$
$570$	−0.101080	+	2.06115i	−0.00423376	+	0.0863321i
$571$	12.3631	−	41.2957i	0.517381	−	1.72817i	−0.154951	−	0.987922i	$-0.549522\pi$
$571$	12.3631	−	41.2957i	0.517381	−	1.72817i	0.672332	−	0.740250i	$-0.265293\pi$
$572$	12.8558	−	8.45539i	0.537528	−	0.353538i
$573$	−13.8675	−	6.80588i	−0.579322	−	0.284320i
$574$	2.38838	−	2.53153i	0.0996891	−	0.105664i
$575$	0.419456	−	0.152669i	0.0174925	−	0.00636676i
$576$	2.70516	+	1.29697i	0.112715	+	0.0540405i
$577$	15.3740	+	5.59569i	0.640029	+	0.232951i	0.641591	−	0.767047i	$-0.278275\pi$
$577$	15.3740	+	5.59569i	0.640029	+	0.232951i	−0.00156160	+	0.999999i	$0.500497\pi$
$578$	15.1199	−	7.59348i	0.628904	−	0.315847i
$579$	42.3767	+	14.9849i	1.76111	+	0.622752i
$580$	6.88584	+	15.9632i	0.285919	+	0.662835i
$581$	−10.6833	−	1.24870i	−0.443219	−	0.0518048i
$582$	12.5592	−	22.2216i	0.520594	−	0.921113i
$583$	−36.1385	−	23.7687i	−1.49671	−	0.984398i
$584$	7.71172	−	6.47090i	0.319113	−	0.267768i
$585$	3.12337	−	19.8357i	0.129135	−	0.820103i
$586$	−15.0317	−	12.6131i	−0.620954	−	0.521043i
$587$	−8.48486	−	28.3414i	−0.350208	−	1.16977i	−0.933820	−	0.357743i	$-0.883547\pi$
$587$	−8.48486	−	28.3414i	−0.350208	−	1.16977i	0.583613	−	0.812032i	$-0.301639\pi$
$588$	7.76271	+	8.07818i	0.320129	+	0.333138i
$589$	3.04661	+	1.53007i	0.125533	+	0.0630453i
$590$	−15.4286	−	16.3534i	−0.635185	−	0.673257i
$591$	−5.64230	+	6.09152i	−0.232093	+	0.250571i
$592$	−1.72504	+	3.99910i	−0.0708989	+	0.164362i
$593$	−1.92938	+	3.34178i	−0.0792301	+	0.137231i	−0.902918	−	0.429813i	$-0.858580\pi$
$593$	−1.92938	+	3.34178i	−0.0792301	+	0.137231i	0.823688	+	0.567043i	$0.191913\pi$
$594$	15.1268	−	21.5317i	0.620658	−	0.883457i
$595$	0.227791	+	0.394545i	0.00933850	+	0.0161748i
$596$	11.4330	−	1.33632i	0.468312	−	0.0547379i
$597$	6.87963	−	16.3599i	0.281564	−	0.669568i
$598$	−8.95927	+	2.12338i	−0.366372	+	0.0868317i
$599$	−0.741474	−	12.7306i	−0.0302958	−	0.520159i	−0.978983	−	0.203942i	$-0.934624\pi$
$599$	−0.741474	−	12.7306i	−0.0302958	−	0.520159i	0.948687	−	0.316216i	$-0.102413\pi$
$600$	0.150473	−	0.206041i	0.00614303	−	0.00841158i
$601$	−15.2965	−	3.62535i	−0.623959	−	0.147881i	−0.0935383	−	0.995616i	$-0.529818\pi$
$601$	−15.2965	−	3.62535i	−0.623959	−	0.147881i	−0.530420	+	0.847735i	$0.677966\pi$
$602$	0.815637	−	4.62571i	0.0332429	−	0.188530i
$603$	−10.2869	−	32.1977i	−0.418913	−	1.31119i
$604$	−2.44400	−	13.8606i	−0.0994450	−	0.563981i
$605$	−1.87591	+	32.2081i	−0.0762666	+	1.30945i
$606$	−19.9811	+	7.48089i	−0.811679	+	0.303890i
$607$	−16.2984	+	21.8926i	−0.661533	+	0.888593i	−0.998600	−	0.0528875i	$-0.983158\pi$
$607$	−16.2984	+	21.8926i	−0.661533	+	0.888593i	0.337068	+	0.941480i	$0.390565\pi$
$608$	0.322975	−	0.433830i	0.0130984	−	0.0175941i
$609$	−9.33454	+	3.49483i	−0.378254	+	0.141618i
$610$	−1.78037	+	30.5678i	−0.0720851	+	1.23765i
$611$	6.02590	+	34.1746i	0.243782	+	1.38256i
$612$	0.572443	−	0.629508i	0.0231396	−	0.0254464i
$613$	6.48791	−	36.7948i	0.262044	−	1.48613i	−0.515278	−	0.857023i	$-0.672311\pi$
$613$	6.48791	−	36.7948i	0.262044	−	1.48613i	0.777322	−	0.629103i	$-0.216578\pi$
$614$	14.4366	+	3.42154i	0.582614	+	0.138082i
$615$	10.7406	−	14.7070i	0.433103	−	0.593043i
$616$	−0.214710	−	3.68643i	−0.00865092	−	0.148531i
$617$	−21.0226	+	4.98245i	−0.846338	+	0.200586i	−0.630835	−	0.775917i	$-0.717287\pi$
$617$	−21.0226	+	4.98245i	−0.846338	+	0.200586i	−0.215504	+	0.976503i	$0.569139\pi$
$618$	−4.13985	+	9.84469i	−0.166529	+	0.396011i
$619$	37.1172	−	4.33838i	1.49187	−	0.174374i	0.669278	−	0.743012i	$-0.266603\pi$
$619$	37.1172	−	4.33838i	1.49187	−	0.174374i	0.822588	+	0.568638i	$0.192529\pi$
$620$	6.94290	+	12.0255i	0.278833	+	0.482954i
$621$	−12.9124	+	9.01139i	−0.518157	+	0.361615i
$622$	−1.40388	+	2.43159i	−0.0562905	+	0.0974980i
$623$	1.11342	−	2.58119i	0.0446081	−	0.103413i
$624$	−3.57624	+	3.86096i	−0.143164	+	0.154562i
$625$	16.6357	+	17.6328i	0.665429	+	0.705313i
$626$	−22.4726	−	11.2862i	−0.898187	−	0.451086i
$627$	−3.28707	−	3.42066i	−0.131273	−	0.136608i
$628$	2.04602	+	6.83419i	0.0816451	+	0.272714i
$629$	0.946261	+	0.794008i	0.0377299	+	0.0316592i
$630$	−3.74771	−	3.02926i	−0.149312	−	0.120689i
$631$	−0.478873	+	0.401822i	−0.0190636	+	0.0159963i	−0.652270	−	0.757987i	$-0.726183\pi$
$631$	−0.478873	+	0.401822i	−0.0190636	+	0.0159963i	0.633206	+	0.773983i	$0.281739\pi$
$632$	−6.68959	−	4.39981i	−0.266098	−	0.175015i
$633$	13.1951	−	23.3468i	0.524459	−	0.927952i
$634$	−17.4523	−	2.03988i	−0.693118	−	0.0810138i
$635$	−9.12164	−	21.1463i	−0.361981	−	0.839167i
$636$	13.9476	+	4.93205i	0.553059	+	0.195568i
$637$	−17.5631	+	8.82052i	−0.695875	+	0.349482i
$638$	−37.5557	−	13.6692i	−1.48684	−	0.541167i
$639$	3.06821	+	40.0130i	0.121376	+	1.58289i
$640$	2.07003	−	0.753431i	0.0818253	−	0.0297820i
$641$	−27.1086	+	28.7334i	−1.07072	+	1.13490i	−0.0803111	+	0.996770i	$0.525591\pi$
$641$	−27.1086	+	28.7334i	−1.07072	+	1.13490i	−0.990414	+	0.138132i	$0.955890\pi$
$642$	−9.92791	−	4.87242i	−0.391823	−	0.192299i
$643$	4.46722	−	2.93814i	0.176170	−	0.115869i	−0.458361	−	0.888766i	$-0.651563\pi$
$643$	4.46722	−	2.93814i	0.176170	−	0.115869i	0.634531	+	0.772897i	$0.281193\pi$
$644$	−0.633733	+	2.11681i	−0.0249726	+	0.0834142i
$645$	1.20386	−	24.5484i	0.0474020	−	0.966591i
$646$	−0.0916027	−	0.123044i	−0.00360406	−	0.00484109i
$647$	18.0471			0.709506			0.354753	−	0.934960i	$-0.384565\pi$
$647$	18.0471			0.709506			0.354753	+	0.934960i	$0.384565\pi$
$648$	−3.25905	+	8.38919i	−0.128028	+	0.329559i
$649$	51.6850			2.02881
$650$	0.267273	+	0.359010i	0.0104833	+	0.0140815i
$651$	−7.08124	+	3.63808i	−0.277536	+	0.142588i
$652$	3.54476	−	11.8403i	0.138824	−	0.463703i
$653$	29.4880	−	19.3945i	1.15395	−	0.758967i	0.179544	−	0.983750i	$-0.442538\pi$
$653$	29.4880	−	19.3945i	1.15395	−	0.758967i	0.974409	+	0.224783i	$0.0721673\pi$
$654$	13.3055	−	8.92716i	0.520287	−	0.349079i
$655$	−10.3789	+	11.0010i	−0.405536	+	0.429843i
$656$	−4.48516	+	1.63246i	−0.175116	+	0.0637370i
$657$	21.1247	+	21.5832i	0.824153	+	0.842042i
$658$	7.82565	+	2.84830i	0.305076	+	0.111038i
$659$	−14.1457	+	7.10424i	−0.551038	+	0.276742i	−0.702455	−	0.711728i	$-0.747913\pi$
$659$	−14.1457	+	7.10424i	−0.551038	+	0.276742i	0.151417	+	0.988470i	$0.451616\pi$
$660$	−3.52976	−	18.9972i	−0.137396	−	0.739464i
$661$	5.77874	+	13.3966i	0.224767	+	0.521069i	0.992862	−	0.119267i	$-0.0380545\pi$
$661$	5.77874	+	13.3966i	0.224767	+	0.521069i	−0.768095	+	0.640336i	$0.778795\pi$
$662$	−14.2475	−	1.66530i	−0.553745	−	0.0647235i
$663$	0.758146	+	1.28575i	0.0294439	+	0.0499345i
$664$	12.3242	+	8.10574i	0.478271	+	0.314564i
$665$	−0.665517	+	0.558435i	−0.0258076	+	0.0216552i
$666$	−12.3579	−	4.24272i	−0.478857	−	0.164402i
$667$	18.3200	+	15.3723i	0.709351	+	0.595216i
$668$	−0.750866	−	2.50807i	−0.0290519	−	0.0970400i
$669$	9.73548	−	33.6392i	0.376395	−	1.30057i
$670$	−22.1799	−	11.1392i	−0.856884	−	0.430343i
$671$	−48.3050	−	51.2003i	−1.86479	−	1.97657i
$672$	0.373313	+	1.20654i	0.0144009	+	0.0465434i
$673$	−0.929462	+	2.15473i	−0.0358281	+	0.0830589i	−0.935191	−	0.354145i	$-0.884772\pi$
$673$	−0.929462	+	2.15473i	−0.0358281	+	0.0830589i	0.899362	+	0.437204i	$0.144031\pi$
$674$	−5.90163	+	10.2219i	−0.227322	+	0.393733i
$675$	0.650827	+	0.402838i	0.0250503	+	0.0155053i
$676$	1.88391	+	3.26303i	0.0724581	+	0.125501i
$677$	24.7224	−	2.88963i	0.950158	−	0.111058i	0.373127	−	0.927780i	$-0.378285\pi$
$677$	24.7224	−	2.88963i	0.950158	−	0.111058i	0.577031	+	0.816723i	$0.304211\pi$
$678$	5.18919	−	0.654851i	0.199290	−	0.0251494i
$679$	10.4562	−	2.47817i	0.401272	−	0.0951033i
$680$	−0.0363281	−	0.623729i	−0.00139312	−	0.0239189i
$681$	9.67162	+	21.8674i	0.370617	+	0.837960i
$682$	−31.0613	−	7.36165i	−1.18940	−	0.281892i
$683$	−0.177301	+	1.00552i	−0.00678423	+	0.0384753i	−0.988012	−	0.154377i	$-0.950663\pi$
$683$	−0.177301	+	1.00552i	−0.00678423	+	0.0384753i	0.981228	+	0.192853i	$0.0617739\pi$
$684$	1.37176	+	0.866582i	0.0524506	+	0.0331346i
$685$	2.88483	+	16.3607i	0.110224	+	0.625109i
$686$	−0.571029	+	9.80420i	−0.0218020	+	0.374326i
$687$	−5.25705	−	4.32961i	−0.200569	−	0.165185i
$688$	−3.84664	+	5.16693i	−0.146652	+	0.196988i
$689$	−15.4976	+	20.8169i	−0.590412	+	0.793062i
$690$	−1.90318	+	11.4045i	−0.0724528	+	0.434161i
$691$	−0.142840	+	2.45247i	−0.00543389	+	0.0932963i	−0.999935	−	0.0114332i	$-0.996361\pi$
$691$	−0.142840	+	2.45247i	−0.00543389	+	0.0932963i	0.994501	+	0.104729i	$0.0333977\pi$
$692$	0.197770	+	1.12161i	0.00751808	+	0.0426371i
$693$	10.9777	−	1.48779i	0.417008	−	0.0565166i
$694$	5.14349	−	29.1702i	0.195244	−	1.10728i
$695$	−7.71157	−	1.82768i	−0.292517	−	0.0693277i
$696$	13.5908	+	1.46225i	0.515157	+	0.0554263i
$697$	0.0787123	+	1.35144i	0.00298144	+	0.0511893i
$698$	9.51219	−	2.25443i	0.360042	−	0.0853314i
$699$	4.14929	+	5.46798i	0.156940	+	0.206818i
$700$	0.106684	−	0.0124696i	0.00403229	−	0.000471308i
$701$	−4.14382	−	7.17731i	−0.156510	−	0.271083i	0.777098	−	0.629380i	$-0.216691\pi$
$701$	−4.14382	−	7.17731i	−0.156510	−	0.271083i	−0.933608	+	0.358296i	$0.883358\pi$
$702$	−12.3693	−	9.81173i	−0.466848	−	0.370320i
$703$	−1.17779	+	2.03999i	−0.0444211	+	0.0769395i
$704$	−2.00581	+	4.64999i	−0.0755968	+	0.175253i
$705$	42.4923	+	9.65991i	1.60035	+	0.363813i
$706$	22.1551	+	23.4831i	0.833819	+	0.883796i
$707$	−8.02674	−	4.03118i	−0.301876	−	0.151608i
$708$	−17.1628	+	4.23436i	−0.645016	+	0.159137i
$709$	1.38745	+	4.63442i	0.0521069	+	0.174049i	0.980082	−	0.198593i	$-0.0636371\pi$
$709$	1.38745	+	4.63442i	0.0521069	+	0.174049i	−0.927975	+	0.372642i	$0.878452\pi$
$710$	22.5735	+	18.9414i	0.847167	+	0.710858i
$711$	11.6264	−	21.0192i	0.436025	−	0.788282i
$712$	−2.95321	+	2.47804i	−0.110676	+	0.0928683i
$713$	15.9590	+	10.4964i	0.597671	+	0.393094i
$714$	0.358193	−	0.00328703i	0.0134050	−	0.000123014i
$715$	33.6670	+	3.93511i	1.25907	+	0.147165i
$716$	−7.94482	−	18.4182i	−0.296912	−	0.688319i
$717$	1.68694	−	1.44210i	0.0630000	−	0.0538561i
$718$	21.6579	−	10.8770i	0.808265	−	0.405926i
$719$	−32.6995	−	11.9017i	−1.21949	−	0.443857i	−0.349502	−	0.936936i	$-0.613649\pi$
$719$	−32.6995	−	11.9017i	−1.21949	−	0.443857i	−0.869985	+	0.493079i	$0.835871\pi$
$720$	2.72847	+	6.01911i	0.101684	+	0.224319i
$721$	−4.22493	+	1.53775i	−0.157345	+	0.0572687i
$722$	−12.8379	+	13.6073i	−0.477775	+	0.506412i
$723$	−2.06988	−	30.6849i	−0.0769797	−	1.14118i
$724$	−14.7302	+	9.68823i	−0.547445	+	0.360060i
$725$	0.333411	−	1.11367i	0.0123826	−	0.0413607i
$726$	21.3209	+	13.7443i	0.791292	+	0.510101i
$727$	−5.15568	−	6.92528i	−0.191214	−	0.256844i	0.696169	−	0.717878i	$-0.254886\pi$
$727$	−5.15568	−	6.92528i	−0.191214	−	0.256844i	−0.887383	+	0.461033i	$0.847479\pi$
$728$	−2.21558			−0.0821147
$729$	−25.8414	−	7.82432i	−0.957090	−	0.289790i
$730$	22.1763			0.820781
$731$	1.09099	+	1.46546i	0.0403518	+	0.0542018i
$732$	20.2350	+	13.0444i	0.747908	+	0.482133i
$733$	−5.01385	+	16.7474i	−0.185191	+	0.618581i	0.814093	+	0.580735i	$0.197235\pi$
$733$	−5.01385	+	16.7474i	−0.185191	+	0.618581i	−0.999284	+	0.0378457i	$0.987950\pi$
$734$	−7.58224	+	4.98691i	−0.279865	+	0.184070i
$735$	1.66103	+	24.6239i	0.0612680	+	0.908265i
$736$	2.07953	−	2.20417i	0.0766524	−	0.0812468i
$737$	53.6169	−	19.5149i	1.97500	−	0.718842i
$738$	−5.91180	−	13.0416i	−0.217616	−	0.480070i
$739$	−10.2783	−	3.74100i	−0.378094	−	0.137615i	0.145980	−	0.989287i	$-0.453366\pi$
$739$	−10.2783	−	3.74100i	−0.378094	−	0.137615i	−0.524074	+	0.851673i	$0.675589\pi$
$740$	−8.57370	+	4.30587i	−0.315175	+	0.158287i
$741$	−2.16357	+	1.84954i	−0.0794806	+	0.0679447i
$742$	2.46684	+	5.71877i	0.0905605	+	0.209943i
$743$	−24.7141	−	2.88867i	−0.906674	−	0.105975i	−0.350042	−	0.936734i	$-0.613833\pi$
$743$	−24.7141	−	2.88867i	−0.906674	−	0.105975i	−0.556632	+	0.830759i	$0.687907\pi$
$744$	10.9175	−	0.100186i	0.400253	−	0.00367301i
$745$	21.1854	+	13.9339i	0.776174	+	0.510497i
$746$	−9.85786	+	8.27173i	−0.360922	+	0.302850i
$747$	−21.4193	+	38.7235i	−0.783690	+	1.41682i
$748$	1.10027	+	0.923239i	0.0402300	+	0.0337570i
$749$	−1.33530	−	4.46020i	−0.0487907	−	0.162972i
$750$	19.0678	−	4.70437i	0.696258	−	0.171779i
$751$	13.1352	+	6.59674i	0.479310	+	0.240718i	0.672014	−	0.740539i	$-0.265430\pi$
$751$	13.1352	+	6.59674i	0.479310	+	0.240718i	−0.192704	+	0.981257i	$0.561726\pi$
$752$	−7.83749	−	8.30725i	−0.285804	−	0.302934i
$753$	18.0784	+	4.10982i	0.658813	+	0.149770i
$754$	−9.49768	+	22.0181i	−0.345885	+	0.801852i
$755$	15.5022	−	26.8506i	0.564182	−	0.977193i
$756$	−3.52341	+	1.39340i	−0.128145	+	0.0506776i
$757$	3.60161	+	6.23818i	0.130903	+	0.226730i	0.924025	−	0.382332i	$-0.124879\pi$
$757$	3.60161	+	6.23818i	0.130903	+	0.226730i	−0.793122	+	0.609063i	$0.791546\pi$
$758$	−17.8364	+	2.08477i	−0.647847	+	0.0757224i
$759$	−16.0675	−	21.1739i	−0.583212	−	0.768564i
$760$	1.15932	−	0.274764i	0.0420530	−	0.00996674i
$761$	−2.66545	−	45.7641i	−0.0966227	−	1.65895i	−0.603823	−	0.797119i	$-0.706356\pi$
$761$	−2.66545	−	45.7641i	−0.0966227	−	1.65895i	0.507200	−	0.861828i	$-0.330681\pi$
$762$	−18.0036	−	1.93703i	−0.652203	−	0.0701712i
$763$	6.56366	+	1.55562i	0.237620	+	0.0563171i
$764$	−1.54871	+	8.78315i	−0.0560302	+	0.317763i
$765$	1.85738	−	0.251728i	0.0671536	−	0.00910126i
$766$	3.91201	+	22.1861i	0.141347	+	0.801618i
$767$	1.80310	−	30.9581i	0.0651063	−	1.11783i
$768$	0.285102	−	1.70843i	0.0102877	−	0.0616475i
$769$	11.6821	−	15.6918i	0.421267	−	0.565860i	−0.539935	−	0.841707i	$-0.681551\pi$
$769$	11.6821	−	15.6918i	0.421267	−	0.565860i	0.961201	+	0.275847i	$0.0889584\pi$
$770$	4.85761	−	6.52491i	0.175056	−	0.235141i
$771$	12.8663	+	10.5964i	0.463368	+	0.381621i
$772$	1.50890	−	25.9069i	0.0543067	−	0.932409i
$773$	−4.95151	−	28.0814i	−0.178093	−	1.01002i	−0.934512	−	0.355930i	$-0.884164\pi$
$773$	−4.95151	−	28.0814i	−0.178093	−	1.01002i	0.756419	−	0.654087i	$-0.226947\pi$
$774$	−16.3377	−	10.3210i	−0.587247	−	0.370981i
$775$	0.161236	−	0.914416i	0.00579177	−	0.0328468i
$776$	−14.3397	−	3.39857i	−0.514765	−	0.122001i
$777$	−2.22495	−	5.03057i	−0.0798195	−	0.180471i
$778$	1.11081	+	19.0719i	0.0398245	+	0.683761i
$779$	−2.51191	+	0.595333i	−0.0899984	+	0.0213300i
$780$	−11.5020	+	1.45150i	−0.411838	+	0.0519720i
$781$	−67.2842	+	7.86440i	−2.40762	+	0.281410i
$782$	−0.429731	−	0.744316i	−0.0153672	−	0.0266167i
$783$	−1.25662	+	40.9884i	−0.0449079	+	1.46481i
$784$	3.23415	−	5.60171i	0.115505	−	0.200061i
$785$	−6.22444	+	14.4299i	−0.222160	+	0.515024i
$786$	3.51496	+	11.3603i	0.125374	+	0.405209i
$787$	22.4749	+	23.8220i	0.801144	+	0.849163i	0.991167	−	0.132617i	$-0.0423379\pi$
$787$	22.4749	+	23.8220i	0.801144	+	0.849163i	−0.190024	+	0.981780i	$0.560856\pi$
$788$	4.28391	+	2.15146i	0.152608	+	0.0766427i
$789$	7.64286	−	26.4085i	0.272093	−	0.940169i
$790$	−5.05866	−	16.8971i	−0.179979	−	0.601172i
$791$	1.68678	+	1.41538i	0.0599750	+	0.0503250i
$792$	−14.3692	−	4.93326i	−0.510587	−	0.175296i
$793$	−32.3529	+	27.1473i	−1.14889	+	0.964031i
$794$	17.2430	+	11.3409i	0.611931	+	0.402473i
$795$	16.5530	+	28.0725i	0.587073	+	0.995628i
$796$	−10.1773	−	1.18955i	−0.360724	−	0.0421626i
$797$	13.5878	+	31.5001i	0.481304	+	1.11579i	0.969949	+	0.243306i	$0.0782321\pi$
$797$	13.5878	+	31.5001i	0.481304	+	1.11579i	−0.488645	+	0.872483i	$0.662509\pi$
$798$	0.124784	+	0.671590i	0.00441732	+	0.0237740i
$799$	−2.89467	+	1.45376i	−0.102406	+	0.0514302i
$800$	−0.138420	−	0.0503808i	−0.00489389	−	0.00178123i
$801$	−8.08972	−	8.26531i	−0.285836	−	0.292040i
$802$	21.2002	−	7.71626i	0.748606	−	0.272470i
$803$	−34.9850	+	37.0819i	−1.23459	+	1.30859i
$804$	−16.2055	+	10.8729i	−0.571523	+	0.383456i
$805$	−4.06681	+	2.67478i	−0.143336	+	0.0942737i
$806$	−5.49307	+	18.3481i	−0.193485	+	0.646286i
$807$	7.02572	−	3.60956i	0.247317	−	0.127062i
$808$	7.35588	+	9.88067i	0.258779	+	0.347601i
$809$	−11.7115			−0.411755			−0.205877	−	0.978578i	$-0.566005\pi$
$809$	−11.7115			−0.411755			−0.205877	+	0.978578i	$0.566005\pi$
$810$	−17.3787	+	9.54205i	−0.610624	+	0.335274i
$811$	−39.4189			−1.38418			−0.692092	−	0.721810i	$-0.743311\pi$
$811$	−39.4189			−1.38418			−0.692092	+	0.721810i	$0.743311\pi$
$812$	3.43643	+	4.61592i	0.120595	+	0.161987i
$813$	−0.0115714	+	0.235956i	−0.000405827	+	0.00827535i
$814$	6.32570	−	21.1293i	0.221716	−	0.740582i
$815$	22.7476	−	14.9613i	0.796813	−	0.524072i
$816$	−0.440999	−	0.216434i	−0.0154381	−	0.00757670i
$817$	−2.39083	+	2.53413i	−0.0836444	+	0.0886579i
$818$	−28.8989	+	10.5183i	−1.01043	+	0.367765i
$819$	−0.508181	−	6.62727i	−0.0177573	−	0.231576i
$820$	−9.88028	−	3.59613i	−0.345034	−	0.125582i
$821$	−39.5505	+	19.8630i	−1.38032	+	0.693223i	−0.975259	−	0.221066i	$-0.929046\pi$
$821$	−39.5505	+	19.8630i	−1.38032	+	0.693223i	−0.405062	+	0.914289i	$0.632750\pi$
$822$	12.3150	+	4.35474i	0.429535	+	0.151889i
$823$	7.64021	+	17.7120i	0.266321	+	0.617401i	0.997929	−	0.0643240i	$-0.0204891\pi$
$823$	7.64021	+	17.7120i	0.266321	+	0.617401i	−0.731608	+	0.681725i	$0.761230\pi$
$824$	6.12424	+	0.715821i	0.213348	+	0.0249368i
$825$	−0.635732	+	1.12483i	−0.0221333	+	0.0391616i
$826$	−6.21774	−	4.08947i	−0.216343	−	0.142291i
$827$	−10.8115	+	9.07193i	−0.375953	+	0.315462i	−0.811111	−	0.584892i	$-0.801137\pi$
$827$	−10.8115	+	9.07193i	−0.375953	+	0.315462i	0.435158	+	0.900354i	$0.356692\pi$
$828$	7.07013	+	5.71475i	0.245704	+	0.198601i
$829$	32.0432	+	26.8874i	1.11290	+	0.933838i	0.998224	−	0.0595644i	$-0.0189712\pi$
$829$	32.0432	+	26.8874i	1.11290	+	0.933838i	0.114680	+	0.993402i	$0.463416\pi$
$830$	9.31952	+	31.1294i	0.323485	+	1.08052i
$831$	−16.2294	−	16.8890i	−0.562993	−	0.585873i
$832$	2.71526	+	1.36365i	0.0941346	+	0.0472762i
$833$	−1.25894	−	1.33440i	−0.0436198	−	0.0462343i
$834$	−4.23441	+	4.57154i	−0.146626	+	0.158299i
$835$	2.28430	−	5.29560i	0.0790514	−	0.183262i
$836$	−1.36948	+	2.37201i	−0.0473645	+	0.0820377i
$837$	2.80379	+	32.6335i	0.0969132	+	1.12798i
$838$	−8.87235	−	15.3674i	−0.306490	−	0.530857i
$839$	15.6086	−	1.82438i	0.538868	−	0.0629846i	0.157694	−	0.987488i	$-0.449594\pi$
$839$	15.6086	−	1.82438i	0.538868	−	0.0629846i	0.381174	+	0.924503i	$0.375520\pi$
$840$	−1.07848	+	2.56466i	−0.0372111	+	0.0884891i
$841$	32.3853	−	7.67546i	1.11674	−	0.264671i
$842$	−0.0454972	−	0.781157i	−0.00156794	−	0.0269205i
$843$	−1.64418	+	2.25135i	−0.0566285	+	0.0775407i
$844$	−15.0658	−	3.57066i	−0.518586	−	0.122907i
$845$	−1.44129	+	8.17398i	−0.0495820	+	0.281193i
$846$	23.0511	−	25.3491i	0.792515	−	0.871518i
$847$	1.85445	+	10.5171i	0.0637195	+	0.361371i
$848$	0.496632	−	8.52684i	0.0170544	−	0.292813i
$849$	−2.47426	+	0.926356i	−0.0849163	+	0.0317925i
$850$	−0.0249484	+	0.0335115i	−0.000855722	+	0.00114943i
$851$	−7.88124	+	10.5863i	−0.270166	+	0.362895i
$852$	21.6984	−	8.12383i	0.743375	−	0.278318i
$853$	0.454052	−	7.79578i	0.0155465	−	0.266922i	−0.981574	−	0.191084i	$-0.938800\pi$
$853$	0.454052	−	7.79578i	0.0155465	−	0.266922i	0.997120	−	0.0758383i	$-0.0241633\pi$
$854$	1.76000	+	9.98146i	0.0602260	+	0.341558i
$855$	1.08779	+	3.40476i	0.0372016	+	0.116440i
$856$	−1.10874	+	6.28798i	−0.0378959	+	0.214919i
$857$	−34.4120	−	8.15579i	−1.17549	−	0.278597i	−0.403953	−	0.914780i	$-0.632364\pi$
$857$	−34.4120	−	8.15579i	−1.17549	−	0.278597i	−0.771538	+	0.636183i	$0.780512\pi$
$858$	15.7183	−	21.5228i	0.536613	−	0.734777i
$859$	2.33567	+	40.1018i	0.0796919	+	1.36826i	0.766886	+	0.641783i	$0.221805\pi$
$859$	2.33567	+	40.1018i	0.0796919	+	1.36826i	−0.687194	+	0.726474i	$0.741158\pi$
$860$	−13.8075	+	3.27245i	−0.470833	+	0.111590i
$861$	2.33675	−	5.55686i	0.0796363	−	0.189377i
$862$	−14.3767	+	1.68039i	−0.489671	+	0.0572343i
$863$	−0.0882934	−	0.152929i	−0.00300554	−	0.00520575i	0.864519	−	0.502601i	$-0.167623\pi$
$863$	−0.0882934	−	0.152929i	−0.00300554	−	0.00520575i	−0.867524	+	0.497395i	$0.834290\pi$
$864$	5.17567	+	0.460946i	0.176080	+	0.0156817i
$865$	−1.25444	+	2.17276i	−0.0426524	+	0.0738761i
$866$	2.38960	−	5.53972i	0.0812020	−	0.188247i
$867$	19.9142	−	21.4997i	0.676323	−	0.730169i
$868$	3.15421	+	3.34327i	0.107061	+	0.113478i
$869$	36.2348	+	18.1978i	1.22918	+	0.617318i
$870$	20.8640	+	21.7119i	0.707356	+	0.736103i
$871$	−9.81849	−	32.7960i	−0.332687	−	1.11125i
$872$	−7.08651	−	5.94629i	−0.239980	−	0.201367i
$873$	6.87680	−	43.6726i	0.232744	−	1.47810i
$874$	1.25551	−	1.05350i	0.0424683	−	0.0356351i
$875$	6.90790	+	4.54340i	0.233530	+	0.153595i
$876$	8.57929	−	15.1798i	0.289867	−	0.512877i
$877$	−40.5935	−	4.74470i	−1.37074	−	0.160217i	−0.601347	−	0.798988i	$-0.705369\pi$
$877$	−40.5935	−	4.74470i	−1.37074	−	0.160217i	−0.769397	+	0.638771i	$0.779443\pi$
$878$	4.76455	+	11.0455i	0.160796	+	0.372767i
$879$	−32.0428	−	11.3307i	−1.08078	−	0.382176i
$880$	−9.96914	+	5.00669i	−0.336060	+	0.168775i
$881$	47.9199	+	17.4414i	1.61446	+	0.587616i	0.982315	−	0.187234i	$-0.0599521\pi$
$881$	47.9199	+	17.4414i	1.61446	+	0.587616i	0.632146	+	0.774849i	$0.282174\pi$
$882$	17.4977	+	8.38920i	0.589180	+	0.282479i
$883$	36.1592	−	13.1609i	1.21686	−	0.442899i	0.347779	−	0.937577i	$-0.386936\pi$
$883$	36.1592	−	13.1609i	1.21686	−	0.442899i	0.869077	+	0.494678i	$0.164714\pi$
$884$	0.591383	−	0.626829i	0.0198904	−	0.0210825i
$885$	−34.9581	−	17.1567i	−1.17510	−	0.576717i
$886$	3.89999	−	2.56506i	0.131023	−	0.0861750i
$887$	4.48166	−	14.9698i	0.150479	−	0.502636i	−0.849197	−	0.528076i	$-0.822914\pi$
$887$	4.48166	−	14.9698i	0.150479	−	0.502636i	0.999676	+	0.0254403i	$0.00809877\pi$
$888$	−0.369497	+	7.53454i	−0.0123995	+	0.252843i
$889$	−4.55222	−	6.11469i	−0.152676	−	0.205080i
$890$	−8.49243			−0.284667
$891$	11.4606	−	44.1130i	0.383945	−	1.47784i
$892$	−20.2186			−0.676969
$893$	−3.68866	−	4.95473i	−0.123436	−	0.165804i
$894$	17.7337	−	9.11095i	0.593105	−	0.304716i
$895$	12.6729	−	42.3305i	0.423609	−	1.41495i
$896$	0.609221	−	0.400691i	0.0203526	−	0.0133861i
$897$	−13.2432	+	8.88534i	−0.442177	+	0.296673i
$898$	5.80273	−	6.15054i	0.193640	−	0.205246i
$899$	46.7464	−	17.0143i	1.55908	−	0.567458i
$900$	0.118951	−	0.425600i	0.00396503	−	0.0141867i
$901$	−2.27640	−	0.828542i	−0.0758379	−	0.0276027i
$902$	21.6002	−	10.8480i	0.719208	−	0.361200i
$903$	−1.48619	−	7.99866i	−0.0494571	−	0.266179i
$904$	−1.19606	−	2.77277i	−0.0397803	−	0.0922211i
$905$	−38.5758	−	4.50886i	−1.28230	−	0.149880i
$906$	−12.3820	−	20.9989i	−0.411366	−	0.697643i
$907$	37.4890	+	24.6569i	1.24480	+	0.818720i	0.988987	−	0.148005i	$-0.0472853\pi$
$907$	37.4890	+	24.6569i	1.24480	+	0.818720i	0.255817	+	0.966725i	$0.417656\pi$
$908$	10.5751	−	8.87359i	0.350948	−	0.294481i
$909$	−27.8680	+	24.2694i	−0.924325	+	0.804964i
$910$	−3.73880	−	3.13723i	−0.123940	−	0.103998i
$911$	2.43036	+	8.11797i	0.0805214	+	0.268960i	0.988764	−	0.149483i	$-0.0477610\pi$
$911$	2.43036	+	8.11797i	0.0805214	+	0.268960i	−0.908243	+	0.418443i	$0.862576\pi$
$912$	0.260426	−	0.899857i	0.00862358	−	0.0297973i
$913$	−66.7550	−	33.5256i	−2.20927	−	1.10954i
$914$	23.2400	+	24.6329i	0.768709	+	0.814784i
$915$	15.6761	+	50.6650i	0.518236	+	1.67493i
$916$	−1.55739	+	3.61044i	−0.0514576	+	0.119292i
$917$	−2.50315	+	4.33558i	−0.0826612	+	0.143173i
$918$	0.546250	−	1.36877i	0.0180289	−	0.0451761i
$919$	16.3656	+	28.3461i	0.539852	+	0.935052i	0.998911	+	0.0466460i	$0.0148533\pi$
$919$	16.3656	+	28.3461i	0.539852	+	0.935052i	−0.459059	+	0.888406i	$0.651813\pi$
$920$	6.63029	−	0.774970i	0.218594	−	0.0255500i
$921$	25.4954	−	3.21740i	0.840102	−	0.106017i
$922$	−15.0508	+	3.56709i	−0.495670	+	0.117476i
$923$	2.36328	+	40.5760i	0.0777884	+	1.33558i
$924$	−2.58707	−	5.84933i	−0.0851085	−	0.192429i
$925$	0.624257	+	0.147952i	0.0205254	+	0.00486462i
$926$	6.37961	−	36.1806i	0.209647	−	1.18897i
$927$	−0.736476	+	18.4831i	−0.0241890	+	0.607066i
$928$	−1.37042	−	7.77203i	−0.0449862	−	0.255129i
$929$	−1.81629	+	31.1844i	−0.0595904	+	1.02313i	0.827481	+	0.561494i	$0.189773\pi$
$929$	−1.81629	+	31.1844i	−0.0595904	+	1.02313i	−0.887071	+	0.461633i	$0.847264\pi$
$930$	18.5651	+	15.2899i	0.608775	+	0.501376i
$931$	2.08910	−	2.80614i	0.0684674	−	0.0919677i
$932$	2.36652	−	3.17879i	0.0775180	−	0.104125i
$933$	−0.800499	+	4.79685i	−0.0262072	+	0.157042i
$934$	−0.654568	+	11.2385i	−0.0214181	+	0.367735i
$935$	0.549425	+	3.11594i	0.0179681	+	0.101902i
$936$	−3.45619	+	8.43471i	−0.112969	+	0.275697i
$937$	7.19453	−	40.8022i	0.235035	−	1.33295i	−0.607505	−	0.794316i	$-0.707830\pi$
$937$	7.19453	−	40.8022i	0.235035	−	1.33295i	0.842540	−	0.538634i	$-0.181059\pi$
$938$	−7.99422	−	1.89467i	−0.261021	−	0.0618630i
$939$	−43.3068	−	4.65943i	−1.41326	−	0.152055i
$940$	−1.46286	−	25.1163i	−0.0477132	−	0.819204i
$941$	8.12581	−	1.92585i	0.264894	−	0.0627810i	−0.0960225	−	0.995379i	$-0.530612\pi$
$941$	8.12581	−	1.92585i	0.264894	−	0.0627810i	0.360916	+	0.932598i	$0.382464\pi$
$942$	7.46928	+	9.84311i	0.243362	+	0.320706i
$943$	−14.3659	+	1.67913i	−0.467818	+	0.0546801i
$944$	5.10302	+	8.83870i	0.166089	+	0.287675i
$945$	−7.91882	−	2.63772i	−0.257599	−	0.0858051i
$946$	16.3106	−	28.2507i	0.530302	−	0.918510i
$947$	12.9550	−	30.0330i	0.420980	−	0.975940i	−0.567332	−	0.823489i	$-0.692024\pi$
$947$	12.9550	−	30.0330i	0.420980	−	0.975940i	0.988311	−	0.152451i	$-0.0487166\pi$
$948$	−13.5232	−	3.07426i	−0.439212	−	0.0998475i
$949$	20.9907	+	22.2488i	0.681386	+	0.722227i
$950$	−0.0711953	−	0.0357556i	−0.00230988	−	0.00116006i
$951$	−29.5480	+	7.29001i	−0.958159	+	0.236395i
$952$	−0.0593141	−	0.198123i	−0.00192238	−	0.00642120i
$953$	6.16798	+	5.17555i	0.199801	+	0.167653i	0.737199	−	0.675676i	$-0.236148\pi$
$953$	6.16798	+	5.17555i	0.199801	+	0.167653i	−0.537398	+	0.843329i	$0.680593\pi$
$954$	25.6195	−	0.470246i	0.829464	−	0.0152248i
$955$	−15.0503	+	12.6287i	−0.487015	+	0.408654i
$956$	−1.07053	−	0.704102i	−0.0346236	−	0.0227723i
$957$	−69.2201	+	0.635212i	−2.23757	+	0.0205335i
$958$	8.20909	+	0.959505i	0.265224	+	0.0310002i
$959$	2.17809	+	5.04938i	0.0703341	+	0.163053i
$960$	2.90022	−	2.47928i	0.0936042	−	0.0800184i
$961$	7.80467	−	3.91965i	0.251764	−	0.126440i
$962$	−12.4353	−	4.52607i	−0.400929	−	0.145926i
$963$	−19.0630	−	1.87423i	−0.614297	−	0.0603961i
$964$	−16.6853	+	6.07297i	−0.537399	+	0.195597i
$965$	39.2301	−	41.5815i	1.26286	−	1.33855i
$966$	0.257584	+	3.81854i	0.00828762	+	0.122859i
$967$	−16.3656	+	10.7638i	−0.526281	+	0.346140i	−0.784683	−	0.619897i	$-0.787174\pi$
$967$	−16.3656	+	10.7638i	−0.526281	+	0.346140i	0.258402	+	0.966037i	$0.416804\pi$
$968$	4.20043	−	14.0304i	0.135007	−	0.450954i
$969$	−0.223313	−	0.143957i	−0.00717385	−	0.00462457i
$970$	−19.3860	−	26.0399i	−0.622447	−	0.836091i
$971$	29.6978			0.953048			0.476524	−	0.879161i	$-0.341897\pi$
$971$	29.6978			0.953048			0.476524	+	0.879161i	$0.341897\pi$
$972$	−0.191662	+	15.5873i	−0.00614755	+	0.499962i
$973$	−2.62333			−0.0841002
$974$	−13.3687	−	17.9573i	−0.428362	−	0.575389i
$975$	0.651570	+	0.420030i	0.0208669	+	0.0134517i
$976$	3.98650	−	13.3158i	0.127605	−	0.426230i
$977$	1.51508	−	0.996484i	0.0484717	−	0.0318804i	−0.525042	−	0.851076i	$-0.675950\pi$
$977$	1.51508	−	0.996484i	0.0484717	−	0.0318804i	0.573514	+	0.819196i	$0.305580\pi$
$978$	−1.44079	−	21.3589i	−0.0460713	−	0.682981i
$979$	13.3975	−	14.2005i	0.428186	−	0.453851i
$980$	13.3896	−	4.87341i	0.427715	−	0.155675i
$981$	16.1612	−	22.5612i	0.515988	−	0.720323i
$982$	12.2102	+	4.44416i	0.389644	+	0.141819i
$983$	15.9237	−	7.99716i	0.507886	−	0.255070i	−0.176354	−	0.984327i	$-0.556430\pi$
$983$	15.9237	−	7.99716i	0.507886	−	0.255070i	0.684240	+	0.729257i	$0.260134\pi$
$984$	−6.28392	+	5.37187i	−0.200324	+	0.171249i
$985$	4.18269	+	9.69657i	0.133272	+	0.308958i
$986$	−2.22319	−	0.259853i	−0.0708007	−	0.00827541i
$987$	14.4237	−	0.132362i	0.459112	−	0.00421313i
$988$	1.37300	+	0.903038i	0.0436810	+	0.0287295i
$989$	−14.9532	+	12.5472i	−0.475483	+	0.398978i
$990$	−17.2627	−	28.6715i	−0.548645	−	0.911240i
$991$	0.979985	+	0.822305i	0.0311303	+	0.0261214i	0.658220	−	0.752826i	$-0.271310\pi$
$991$	0.979985	+	0.822305i	0.0311303	+	0.0261214i	−0.627090	+	0.778947i	$0.715754\pi$
$992$	−1.80785	−	6.03865i	−0.0573994	−	0.191727i
$993$	−24.1221	+	5.95135i	−0.765492	+	0.188860i
$994$	8.71659	+	4.37763i	0.276473	+	0.138850i
$995$	−15.4899	−	16.4183i	−0.491061	−	0.520495i
$996$	24.9136	+	5.66369i	0.789418	+	0.179461i
$997$	−4.55541	+	10.5606i	−0.144271	+	0.334458i	−0.974995	−	0.222227i	$-0.928668\pi$
$997$	−4.55541	+	10.5606i	−0.144271	+	0.334458i	0.830724	+	0.556685i	$0.187927\pi$
$998$	21.0625	−	36.4813i	0.666721	−	1.15480i
$999$	−22.6222	+	0.622932i	−0.715735	+	0.0197087i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.2.g.a.7.2	✓	72
3.2	odd	2		486.2.g.a.343.4		72
81.23	odd	54		486.2.g.a.469.4		72
81.58	even	27	inner	162.2.g.a.139.2	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.2.g.a.7.2	✓	72	1.1	even	1	trivial
162.2.g.a.139.2	yes	72	81.58	even	27	inner
486.2.g.a.343.4		72	3.2	odd	2
486.2.g.a.469.4		72	81.23	odd	54

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	162.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.597159 - 0.802123i) q^{2} +(-1.45578 - 0.938458i) q^{3} +(-0.286803 + 0.957990i) q^{4} +(-1.84048 + 1.21050i) q^{5} +(0.116573 + 1.72812i) q^{6} +(-0.500394 + 0.530386i) q^{7} +(0.939693 - 0.342020i) q^{8} +(1.23859 + 2.73238i) q^{9} +O(q^{10})\)	\(q+(-0.597159 - 0.802123i) q^{2} +(-1.45578 - 0.938458i) q^{3} +(-0.286803 + 0.957990i) q^{4} +(-1.84048 + 1.21050i) q^{5} +(0.116573 + 1.72812i) q^{6} +(-0.500394 + 0.530386i) q^{7} +(0.939693 - 0.342020i) q^{8} +(1.23859 + 2.73238i) q^{9} +(2.07003 + 0.753431i) q^{10} +(-4.52549 + 2.27279i) q^{11} +(1.31656 - 1.12547i) q^{12} +(1.20347 + 2.78995i) q^{13} +(0.724249 + 0.0846526i) q^{14} +(3.81535 - 0.0350123i) q^{15} +(-0.835488 - 0.549509i) q^{16} +(-0.217267 + 0.182309i) q^{17} +(1.45207 - 2.62517i) q^{18} +(-0.414317 - 0.347653i) q^{19} +(-0.631794 - 2.11034i) q^{20} +(1.22621 - 0.302527i) q^{21} +(4.52549 + 2.27279i) q^{22} +(-2.07953 - 2.20417i) q^{23} +(-1.68896 - 0.383956i) q^{24} +(-0.0583439 + 0.135256i) q^{25} +(1.51922 - 2.63137i) q^{26} +(0.761105 - 5.14011i) q^{27} +(-0.364590 - 0.631488i) q^{28} +(-7.83856 + 0.916196i) q^{29} +(-2.30645 - 3.03947i) q^{30} +(-6.13355 + 1.45368i) q^{31} +(0.0581448 + 0.998308i) q^{32} +(8.72104 + 0.938307i) q^{33} +(0.275977 + 0.0654077i) q^{34} +(0.278931 - 1.58190i) q^{35} +(-2.97282 + 0.402903i) q^{36} +(-0.756289 - 4.28913i) q^{37} +(-0.0314478 + 0.539938i) q^{38} +(0.866269 - 5.19096i) q^{39} +(-1.31547 + 1.76698i) q^{40} +(2.85024 - 3.82854i) q^{41} +(-0.974905 - 0.802913i) q^{42} +(0.374544 - 6.43067i) q^{43} +(-0.879381 - 4.98722i) q^{44} +(-5.58716 - 3.52957i) q^{45} +(-0.526208 + 2.98428i) q^{46} +(11.1130 + 2.63384i) q^{47} +(0.700595 + 1.58403i) q^{48} +(0.376098 + 6.45735i) q^{49} +(0.143333 - 0.0339705i) q^{50} +(0.487382 - 0.0615053i) q^{51} +(-3.01790 + 0.352742i) q^{52} +(4.27064 + 7.39697i) q^{53} +(-4.57750 + 2.45896i) q^{54} +(5.57787 - 9.66116i) q^{55} +(-0.288813 + 0.669545i) q^{56} +(0.276897 + 0.894926i) q^{57} +(5.41577 + 5.74038i) q^{58} +(-9.12046 - 4.58047i) q^{59} +(-1.06071 + 3.66510i) q^{60} +(3.98650 + 13.3158i) q^{61} +(4.82873 + 4.05179i) q^{62} +(-2.06900 - 0.710332i) q^{63} +(0.766044 - 0.642788i) q^{64} +(-5.59221 - 3.67806i) q^{65} +(-4.45521 - 7.55567i) q^{66} +(-11.1908 - 1.30802i) q^{67} +(-0.112337 - 0.260426i) q^{68} +(0.958813 + 5.16034i) q^{69} +(-1.43544 + 0.720905i) q^{70} +(12.5701 + 4.57514i) q^{71} +(2.09842 + 2.14397i) q^{72} +(9.45983 - 3.44310i) q^{73} +(-2.98879 + 3.16793i) q^{74} +(0.211868 - 0.142150i) q^{75} +(0.451876 - 0.297203i) q^{76} +(1.05907 - 3.53755i) q^{77} +(-4.68109 + 2.40497i) q^{78} +(-4.78134 - 6.42245i) q^{79} +2.20288 q^{80} +(-5.93178 + 6.76860i) q^{81} -4.77300 q^{82} +(8.80861 + 11.8320i) q^{83} +(-0.0618626 + 1.26146i) q^{84} +(0.179191 - 0.598538i) q^{85} +(-5.38186 + 3.53970i) q^{86} +(12.2710 + 6.02238i) q^{87} +(-3.47523 + 3.68353i) q^{88} +(-3.62265 + 1.31854i) q^{89} +(0.505270 + 6.58931i) q^{90} +(-2.08196 - 0.757772i) q^{91} +(2.70799 - 1.36000i) q^{92} +(10.2933 + 3.63985i) q^{93} +(-4.52358 - 10.4868i) q^{94} +(1.18338 + 0.138317i) q^{95} +(0.852224 - 1.50788i) q^{96} +(-12.3125 - 8.09807i) q^{97} +(4.95500 - 4.15774i) q^{98} +(-11.8154 - 9.55030i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 9 q^{6}+O(q^{10}) \) 72 * q + 9 * q^6	\( 72 q + 9 q^{6} + 18 q^{13} - 9 q^{20} - 81 q^{23} + 18 q^{25} - 27 q^{26} - 27 q^{27} + 18 q^{28} - 27 q^{29} - 63 q^{30} - 54 q^{31} + 9 q^{33} - 27 q^{35} - 9 q^{36} + 9 q^{38} - 9 q^{41} + 9 q^{42} + 36 q^{43} - 117 q^{45} - 18 q^{46} - 27 q^{47} + 9 q^{48} - 27 q^{51} - 36 q^{52} - 27 q^{53} + 54 q^{55} + 27 q^{57} + 9 q^{58} - 18 q^{59} + 9 q^{63} + 9 q^{65} + 36 q^{66} - 135 q^{67} - 18 q^{68} + 108 q^{69} + 18 q^{70} + 72 q^{71} + 54 q^{72} + 36 q^{73} + 99 q^{74} - 36 q^{75} - 9 q^{76} + 144 q^{77} + 90 q^{78} - 9 q^{79} + 18 q^{80} - 72 q^{82} + 99 q^{83} + 18 q^{84} + 9 q^{85} + 72 q^{86} + 207 q^{87} - 9 q^{88} + 126 q^{89} - 18 q^{90} + 63 q^{91} + 36 q^{92} + 81 q^{93} + 18 q^{94} + 45 q^{95} - 171 q^{97} + 36 q^{98} + 99 q^{99}+O(q^{100}) \) 72 * q + 9 * q^6 + 18 * q^13 - 9 * q^20 - 81 * q^23 + 18 * q^25 - 27 * q^26 - 27 * q^27 + 18 * q^28 - 27 * q^29 - 63 * q^30 - 54 * q^31 + 9 * q^33 - 27 * q^35 - 9 * q^36 + 9 * q^38 - 9 * q^41 + 9 * q^42 + 36 * q^43 - 117 * q^45 - 18 * q^46 - 27 * q^47 + 9 * q^48 - 27 * q^51 - 36 * q^52 - 27 * q^53 + 54 * q^55 + 27 * q^57 + 9 * q^58 - 18 * q^59 + 9 * q^63 + 9 * q^65 + 36 * q^66 - 135 * q^67 - 18 * q^68 + 108 * q^69 + 18 * q^70 + 72 * q^71 + 54 * q^72 + 36 * q^73 + 99 * q^74 - 36 * q^75 - 9 * q^76 + 144 * q^77 + 90 * q^78 - 9 * q^79 + 18 * q^80 - 72 * q^82 + 99 * q^83 + 18 * q^84 + 9 * q^85 + 72 * q^86 + 207 * q^87 - 9 * q^88 + 126 * q^89 - 18 * q^90 + 63 * q^91 + 36 * q^92 + 81 * q^93 + 18 * q^94 + 45 * q^95 - 171 * q^97 + 36 * q^98 + 99 * q^99

Introduction

L-functions

Modular forms

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